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How to get exact solution using Maple...

Elisha 55
May 16 2017
0 1

@Carl Love Pls see what I did but seems am not yet home.How can I get numeric solution for values of t=0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5 in this system of ODE?


 

``

> 

odesys := {diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)};

{diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)}

 (1)
> 

v(0) := .4;

.4

 (2)
> 

NULL
> 

s(0) := 0.6e-1;

0.6e-1

 (3)
> 

e[0] := .24;

.24

 (4)
> 

i[0] := .17;

.17

 (5)
> 

r[0] := .13;

.13

 (6)
> 

c := 0.4e-1;

0.4e-1

 (7)
> 

f := .4;

.4

 (8)
> 

beta := .2;

.2

 (9)
> 

epsilon := .8;

.8

 (10)
> 

theta[1] := .1;

.1

 (11)
> 

theta[2] := .3;

.3

 (12)
> 

alpha := .9;

.9

 (13)
> 

rho := .7;

.7

 (14)
> 

eta := .99;

.99

 (15)
> 

delta := .3;

.3

 (16)
> 

a := 0.4e-1;

0.4e-1

 (17)
> 

phi := 1;

1

 (18)
> 

lambda := 0.96e-1;

0.96e-1

 (19)
> 

('`union`')(`~`[indets](odesys)[]);

`union`({t, s(t), v(t), diff(s(t), t)}, {t, s(t), v(t), diff(v(t), t)}, {t, s(t), diff((table( [( 0 ) = .24 ] ))(t), t), (table( [( 0 ) = .24 ] ))(t)}, {t, diff((table( [( 0 ) = .17 ] ))(t), t), (table( [( 0 ) = .17 ] ))(t), (table( [( 0 ) = .24 ] ))(t)}, {t, v(t), diff((table( [( 0 ) = .13 ] ))(t), t), (table( [( 0 ) = .13 ] ))(t), (table( [( 0 ) = .17 ] ))(t)})

 (20)
> 

dsolve(odesys)

Error, (in dsolve) invalid input: D expects its 1st argument, f, to be of type {set, array, list, algebraic, equation, procedure}, but received table( [( 0 ) = .13 ] )

  
> 

``

``


 

Download odesys.mw

How to get exact solution using Maple...

Elisha 55
May 15 2017
0 0

@tomleslie 
How can I get the exact solution for the system below?

``

> 

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t):
> 

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t):
> 

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t):
> 

diff(r(t), t) = eta*i(t)+v(t)*f*theta[2]-(a+epsilon)*r(t)


 

Download SYSTEM_OF_EQUATIONS.mw

How to use 4th orderrungekutta method on...

Elisha 55
May 14 2017
0 3

@Carl Love 
Kindly assist check if what I did is correct. I doubt this figures because it quite high above 1 which is not what I was expecting.

``

> 

f := proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc;

proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc

 (1)
> 

f := proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc;

proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc

 (2)
> 

f := proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc;

proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc

 (3)
> 

f := proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc;

proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc

 (4)
> 

f := proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc;

proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc

 (5)
> 

t[0] := 0:
> 

s[0] := 0.6e-1:
> 

v[0] := .4:
> 

e[0] := .24:
> 

i[0] := .17:
> 

r[0] := .13:
> 

h := .1:
> 

c := 0.4e-1;

0.4e-1

 (6)
> 

f := .4;

.4

 (7)
> 

beta := .2;

.2

 (8)
> 

epsilon := .8;

.8

 (9)
> 

theta[1] := .1;

.1

 (10)
> 

theta[2] := .3;

.3

 (11)
> 

alpha := .9;

.9

 (12)
> 

rho := .7;

.7

 (13)
> 

eta := .99;

.99

 (14)
> 

delta := .3;

.3

 (15)
> 

a := 0.4e-1;

0.4e-1

 (16)
> 

phi := 1;

1

 (17)
> 

lambda := 0.96e-1;

0.96e-1

 (18)
> 

NULL
> 

for n to 10 do t[n] := n*h; k1 := f(t[n-1], s[n-1]); k2 := f(t[n-1]+(1/2)*h, s[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, s[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+s[n-1]); s[n] := s[n-1]+1/6*(k1+2*k2+2*k3+k4) end do;

.1

  

.4

  

.4

  

.4

  

.4

  

.4600000000

  

.2

  

.4

  

.4

  

.4

  

.4

  

.8600000000

  

.3

  

.4

  

.4

  

.4

  

.4

  

1.260000000

  

.4

  

.4

  

.4

  

.4

  

.4

  

1.660000000

  

.5

  

.4

  

.4

  

.4

  

.4

  

2.060000000

  

.6

  

.4

  

.4

  

.4

  

.4

  

2.460000000

  

.7

  

.4

  

.4

  

.4

  

.4

  

2.860000000

  

.8

  

.4

  

.4

  

.4

  

.4

  

3.260000000

  

.9

  

.4

  

.4

  

.4

  

.4

  

3.660000000

  

1.0

  

.4

  

.4

  

.4

  

.4

  

4.060000000

 (19)
> 

NULL
> 

for n to 8 do t[n] := n*h; k1 := f(t[n-1], v[n-1]); k2 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+v[n-1]); v[n] := v[n-1]+1/6*(k1+2*k2+2*k3+k4) end do

.1

  

.4

  

.4

  

.4

  

.4

  

.8000000000

  

.2

  

.4

  

.4

  

.4

  

.4

  

1.200000000

  

.3

  

.4

  

.4

  

.4

  

.4

  

1.600000000

  

.4

  

.4

  

.4

  

.4

  

.4

  

2.000000000

  

.5

  

.4

  

.4

  

.4

  

.4

  

2.400000000

  

.6

  

.4

  

.4

  

.4

  

.4

  

2.800000000

  

.7

  

.4

  

.4

  

.4

  

.4

  

3.200000000

  

.8

  

.4

  

.4

  

.4

  

.4

  

3.600000000

 (20)
> 

NULL
> 

NULL
> 

NULL
> 

``
> 

for n to 8 do t[n] := n*h; k1 := f(t[n-1], e[n-1]); k2 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+e[n-1]); e[n] := e[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

  

.4

  

.4

  

.4

  

.4

  

.6400000000

  

.2

  

.4

  

.4

  

.4

  

.4

  

1.040000000

  

.3

  

.4

  

.4

  

.4

  

.4

  

1.440000000

  

.4

  

.4

  

.4

  

.4

  

.4

  

1.840000000

  

.5

  

.4

  

.4

  

.4

  

.4

  

2.240000000

  

.6

  

.4

  

.4

  

.4

  

.4

  

2.640000000

  

.7

  

.4

  

.4

  

.4

  

.4

  

3.040000000

  

.8

  

.4

  

.4

  

.4

  

.4

  

3.440000000

 (21)
> 

``
> 

``
> 

for n to 8 do t[n] := n*h; k1 := f(t[n-1], i[n-1]); k2 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+i[n-1]); i[n] := i[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

  

.4

  

.4

  

.4

  

.4

  

.5700000000

  

.2

  

.4

  

.4

  

.4

  

.4

  

.9700000000

  

.3

  

.4

  

.4

  

.4

  

.4

  

1.370000000

  

.4

  

.4

  

.4

  

.4

  

.4

  

1.770000000

  

.5

  

.4

  

.4

  

.4

  

.4

  

2.170000000

  

.6

  

.4

  

.4

  

.4

  

.4

  

2.570000000

  

.7

  

.4

  

.4

  

.4

  

.4

  

2.970000000

  

.8

  

.4

  

.4

  

.4

  

.4

  

3.370000000

 (22)
> 

``
> 

NULL
> 

NULL
> 

for n to 8 do t[n] := n*h; k1 := f(t[n-1], r[n-1]); k2 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k1); k3 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k2); k4 := f(t[n-1]+h, h*k3+r[n-1]); r[n] := r[n-1]+1/6*(k1+2*k2+2*k3+k4) end do
NULL

.1

  

.4

  

.4

  

.4

  

.4

  

.5300000000

  

.2

  

.4

  

.4

  

.4

  

.4

  

.9300000000

  

.3

  

.4

  

.4

  

.4

  

.4

  

1.330000000

  

.4

  

.4

  

.4

  

.4

  

.4

  

1.730000000

  

.5

  

.4

  

.4

  

.4

  

.4

  

2.130000000

  

.6

  

.4

  

.4

  

.4

  

.4

  

2.530000000

  

.7

  

.4

  

.4

  

.4

  

.4

  

2.930000000

  

.8

  

.4

  

.4

  

.4

  

.4

  

3.330000000

 (23)
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

``


 

Download runge_and_maple.mw

Runge-Kutta-Fehlberg fourth-fifth-order ...

Elisha 55
May 11 2017
0 0

@Carl Love Thank you for that update. I really will appreciate this recent method if I know how to go about it. Can you pls give me an example using my system of equation above to enable me follow? 

How to use 4th orderrungekutta method on...

Elisha 55
May 10 2017
0 20

@Carl Love
Thank you for your response to my question on Rk4. I am actually doing a comparison between Adomian Decomposition method and Rk4. this error "Error, unable to parse"

is still there.
 

``

> 

f := proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc;

proc (t, s) options operator, arrow; (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v-(lambda+theta[1]+a+epsilon)*s end proc

 (1)
> 

f := proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc;

proc (t, v) options operator, arrow; phi*epsilon+rho*a+theta[1]*s-((1-f)*alpha+f*theta[2]+a+epsilon)*v end proc

 (2)
> 

f := proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc;

proc (t, e) options operator, arrow; `λs`-(delta+a+epsilon)*e end proc

 (3)
> 

f := proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc;

proc (t, i) options operator, arrow; delta*e-(eta+a+epsilon)*i end proc

 (4)
> 

f := proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc;

proc (t, r) options operator, arrow; `ηi`+f*theta[2]*v-(a+epsilon)*r end proc

 (5)
> 

t[0] := 0:
> 

s[0] := 0.6e-1:
> 

v[0] := .4:
> 

e[0] := .24:
> 

i[0] := .17:
> 

r[0] := .13:
> 

h := .1:
> 

c := 0.4e-1;

0.4e-1

 (6)
> 

f := .4;

.4

 (7)
> 

beta := .2;

.2

 (8)
> 

epsilon := .8;

.8

 (9)
> 

theta[1] := .1;

.1

 (10)
> 

theta[2] := .3;

.3

 (11)
> 

alpha := .9;

.9

 (12)
> 

rho := .7;

.7

 (13)
> 

eta := .99;

.99

 (14)
> 

delta := .3;

.3

 (15)
> 

a := 0.4e-1;

0.4e-1

 (16)
> 

phi := 0;

0

 (17)
> 

lambda := 0.96e-1;

0.96e-1

 (18)
> 

NULL
> 

"for n from 1 to 2 do t[n]:=n*h: k1:=f(t[n-1],v[n-1]): k2:=f(t[n-1]+(h/(2)),v[n-1]+(h/(2))*k1): k3:=f(t[n-1]+(h/(2)),s[n-1]+(h/(2))*k2): k4:=f(t[n-1]+h,s[n-1]+h*k3): s[n]:=s[n-1]+(1/(6))*(k1+2 k2+2 k3+k4):"
> 

"od;"

Error, unable to parse

"od;"

  
> 

``

Error, unable to parse

"od;"

  
> 

"for n from 1 to 2 do"
> 

t[n] := n*h
> 

k1 := f(t[n-1], v[n-1])
> 

k2 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k1)
> 

k3 := f(t[n-1]+(1/2)*h, v[n-1]+(1/2)*h*k2)
> 

k4 := f(t[n-1]+h, h*k3+v[n-1])
> 

v[n] := v[n-1]+1/6*(k1+2*k2+2*k3+k4)
> 

"od;"
> 

NULL
> 

``
> 

"for n from 1 to 8 do"
> 

t[n] := n*h
> 

k1 := f(t[n-1], e[n-1])
> 

k2 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k1)
> 

k3 := f(t[n-1]+(1/2)*h, e[n-1]+(1/2)*h*k2)
> 

k4 := f(t[n-1]+h, h*k3+e[n-1])
> 

e[n] := e[n-1]+1/6*(k1+2*k2+2*k3+k4)
> 

"od;"
> 

``
> 

``
> 

"for n from 1 to 8 do"
> 

t[n] := n*h
> 

k1 := f(t[n-1], i[n-1])
> 

k2 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k1)
> 

k3 := f(t[n-1]+(1/2)*h, i[n-1]+(1/2)*h*k2)
> 

k4 := f(t[n-1]+h, h*k3+i[n-1])
> 

i[n] := i[n-1]+1/6*(k1+2*k2+2*k3+k4)
> 

"od;"
> 

``
> 

NULL
> 

NULL
> 

"for n from 1 to 8 do"
> 

t[n] := n*h
> 

k1 := f(t[n-1], r[n-1])
> 

k2 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k1)
> 

k3 := f(t[n-1]+(1/2)*h, r[n-1]+(1/2)*h*k2)
> 

k4 := f(t[n-1]+h, h*k3+r[n-1])
> 

r[n] := r[n-1]+1/6*(k1+2*k2+2*k3+k4)
> 

"od;"
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

``


 

Download runge_and_maple.mw

thank you
Elisha

PLOT...

Elisha 55
April 18 2017
0 0

@ThU 

Thanks Sir,

Your response is quite helpful

Regards.

How to Plot...

Elisha 55
April 18 2017
0 2

@AmusingYeti 

Thanks for you quick and timely response.

Regards

How can I write a Maple code that can ha...

Elisha 55
April 05 2017
0 1

@John May 

Dear John, Thanks for your effort. Find detail of what am trying to do below
 

> 

restart
> 

with(student)
> 

``
> 

G := S(t)*L(t)

S(t)*L(t)

 (1)
> 

m := 10
> 

S[lambda] := sum(S[b]*lambda^b, b = 0 .. m); L[lambda] := sum(L[b]*lambda^b, b = 0 .. m); G[lambda] := subs(S(t) = S[lambda], G); G[lambda] := subs(L(t) = L[lambda], G[lambda]); G := G[lambda]; s := expand(G, lambda); ft := unapply(s, lambda); for i from 0 while i <= m do A1[i] := ((D@@i)(ft))(0)/factorial(i); print(A[i] = A1[i]) end do

A[0] = S[0]*L[0]

  

A[1] = L[0]*S[1]+L[1]*S[0]

  

A[2] = L[0]*S[2]+L[1]*S[1]+L[2]*S[0]

  

A[3] = L[0]*S[3]+L[1]*S[2]+L[2]*S[1]+L[3]*S[0]

  

A[4] = L[0]*S[4]+L[1]*S[3]+L[2]*S[2]+L[3]*S[1]+L[4]*S[0]

  

A[5] = L[0]*S[5]+L[1]*S[4]+L[2]*S[3]+L[3]*S[2]+L[4]*S[1]+L[5]*S[0]

  

A[6] = L[0]*S[6]+L[1]*S[5]+L[2]*S[4]+L[3]*S[3]+L[4]*S[2]+L[5]*S[1]+L[6]*S[0]

  

A[7] = S[5]*L[2]+S[2]*L[5]+S[1]*L[6]+S[0]*L[7]+S[4]*L[3]+S[3]*L[4]+S[6]*L[1]+S[7]*L[0]

  

A[8] = S[2]*L[6]+S[0]*L[8]+S[8]*L[0]+S[4]*L[4]+S[1]*L[7]+S[3]*L[5]+S[6]*L[2]+S[5]*L[3]+S[7]*L[1]

  

A[9] = S[6]*L[3]+S[9]*L[0]+S[4]*L[5]+S[2]*L[7]+S[3]*L[6]+S[8]*L[1]+S[0]*L[9]+S[1]*L[8]+S[7]*L[2]+S[5]*L[4]

  

A[10] = S[0]*L[10]+S[10]*L[0]+S[1]*L[9]+S[6]*L[4]+S[7]*L[3]+S[3]*L[7]+S[2]*L[8]+S[4]*L[6]+S[9]*L[1]+S[5]*L[5]+S[8]*L[2]

 (2)

s[n+1] := (1-f)*alpha*(int(v__n, t = 0 .. t))-beta*c*(int(A__n, t = 0 .. t))-(`&theta;__1`+a+Pi)*(int(s__n, t = 0 .. t))

v[n+1] := `&theta;__1`*(int(s__n, t = 0 .. t))-((1-f)*alpha+f*`&theta;__2`+a+Pi)*(int(v__n, t = 0 .. t))

e[n+1] := `&beta;c`*(int(A__n, t = 0 .. t))-(delta+a+Pi)*(int(e__n, t = 0 .. t))

i[n+1] := delta*(int(e__n, t = 0 .. t))-(eta+a+Pi)*(int(i__n, t = 0 .. t))

r[n+1] := eta*(int(i__n, t = 0 .. t))+`f&theta;__2`*(int(v__n, t = 0 .. t))-(a+Pi)*(int(r__n, t = 0 .. t))

for n from 0 to 4 do end do

``

(1-f)*alpha*v__n*t-beta*c*s__0*i__0*t-(`&theta;__1`+a+Pi)*s__n*t

 (3)

"for n:=0, n=1, n=2, n=3, n=4: `s__1, ``s__2__`, `s__3, ``s__4`, `i__1`, `i__2, ``i__3`, `i__4`, `r__1`, `r__2`, `r__3, ``r__4`:"

Error, unterminated for loop

"for n:=0, n=1, n=2, n=3, n=4: `s__1, ` `s__2__`, `s__3, __3__, s__4`, `i__1__`, `i__2, ` `i__3`, `i__4`, `r__1`, `r__2`, `r__3, ` `r__4`:"

  

and s(t)= s1+s2+s3+s4

i(t) = i__1+`i__2, `+i__3+i__4, r(t) = r__1+r__2+r__3_+r__4

"but A[n]:=(1)/(n!) [((&DifferentialD;)^(n))/(&DifferentialD; lambda^(n)) ((&sum;)`s__k`lambda^(k))((&sum;)`i__k`lambda^(k)) ]() ? ()|() ? (lambda=0)"

Error, missing numerator

Typesetting:-mambiguous(Typesetting:-mrow(Typesetting:-mi("but", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msub(Typesetting:-mi("A", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mi("n", fontstyle = "italic", mathcolor = "#c800c8", mathvariant = "italic", placeholder = "true"), subscriptshift = "0"), Typesetting:-mo("&Assign;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfrac(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&excl;", accent = "false", fence = "false", largeop = "false", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "false", rspace = "0.1111111em", separator = "false", stretchy = "false", symmetric = "false")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-msup(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mrow(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`s__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`i__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false")), open = "&lsqb;", close = "&rsqb;", mathvariant = "normal"), Typesetting:-mfrac(Typesetting:-mambiguous(Typesetting:-merror("?"), Typesetting:-merror("missing numerator")), Typesetting:-mphantom(Typesetting:-mrow(Typesetting:-mi("x", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "unset", rspace = "0.2777778em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic")), constraints = "height-only"), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center"), Typesetting:-mo("&verbar;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "unset", rspace = "0.1111111em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mfrac(Typesetting:-mphantom(Typesetting:-mi("f(x)", fontstyle = "italic", mathvariant = "italic"), constraints = "height-only"), Typesetting:-mrow(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center")))

  

NULL

> The one highlighted in red is the error that was generated wthen i tried generating the values of s1,s2,s3,s4 ; i1,i2,i3,i4 and r1,r2,r3,r4

> 

NULL
> 

> 

> 

``
> 

``


 

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