assma

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5 years, 85 days

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These are questions asked by assma

the error in summation , How can this be corrected?

restart;

U[0] := x^2;

for k from 0 to 1 do U[k+1] := sum(U[s]*(diff(U[k-s], x)), s = 0 .. k) end do;
U[0]*(diff(U[0], x));
                                 3
                              2 x 
U[1];
                               0

How can the value of uu(.1, .1, .1)  as a number, and what is the error when drawing?

restart;
uu := proc (x, y, t) options operator, arrow; e^(.2*t)*(e^(-x)+e^(-y)) end proc;

evalf(uu(.1, .1, .1));
                              2.  
                             -----
                              0.08
                             e    
plot3d(uu(x, y, .1), x = 1 .. 2, y = 1 .. 2);
Warning, expecting only range variables [x, y] in expression e^.2e-1*(e^(-x)+e^(-y)) to be plotted but found name e

how can revision of error in 

restart;
u0 := proc (x) options operator, arrow; 1+2*x end proc; h := 0;
for k from 0 to 5 do U := proc (k, h) options operator, arrow; eval((diff(u0(x), [`$`(x, k)]))/factorial(k), x = 0) end proc end do;
m := h+1;
for k from 0 to 5 do U := proc (k, h) options operator, arrow; (sum(sum(U(r, h-s)*U(k-r, s), s = 0 .. h), r = 0 .. k)+(k+1)*U(k, h))/m end proc end do;
U(0, 1);
Error, (in U) too many levels of recursion

 

How to draw the given data?


 

 

restart

``

0, 0.

 

0.5e-1, 0.7453559923e-1

 

.10, .1054092553

 

.15, .1290994449

 

.20, .1490711985

 

.25, .1666666667

 

.30, .1825741858

 

.35, .1972026594

 

.40, .2108185107

 

.45, .2236067977

 

.50, .2357022604

 

.55, .2472066162

 

.60, .2581988897

 

.65, .2687419249

 

.70, .2788866755

 

.75, .2886751346

 

.80, .2981423970

 

.85, .3073181486

 

.90, .3162277660

 

.95, .3248931448

 

1.00, .3333333333

 

``


 

Download aaa.mw

 

 


How to solve a system of partial equations with boundary conditions.I used this formula

restart;
sys_Pde := diff(V(x, t), x, x) = 0, diff(T(x, t), x, x) = 0;
          
BC := eval(diff(V(x, t), x), x = 1) = 0, eval(V(x, t), x = 0) = 1+cos(w*t), eval(T(x, t), x = 0) = 0, eval(T(x, t), x = 1) = 1;
pdsolve({sys_Pde});
   {T(x, t) = _F1(t) x + _F2(t), V(x, t) = _F3(t) x + _F4(t)}
pdsolve({BC, sys_Pde});


Error, (in PDEtools:-ToJet) found functions to be rewritten in jet notation, {V(1, t)}, having different dependency than the indicated in [V(x, t)]

 

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