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Question: Comparing RK4 and RK45. How to solve Differential equation using the fouth order Runge-kutta RK4

Question:Comparing RK4 and RK45. How to solve Differential equation using the fouth order Runge-kutta RK4

Elisha 55 Maple
ode homework dsolve numeric differential-equations runge-kutta duplicate-question
January 08 2018
0

Dear Team, I have used RKF45 to solve my ODE with Maple. now I am required to solve same ODE using RK4 for comparison of solution. Ps help me with an example. Pls find my Parameters, intial values and ODE below:


 

``

> 

ODE*equations

ODE*equations

 (1)
> 

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)
> 

NULL
> 

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

``
> 

``
> 

My*parameters

My*parameters

 (2)
> 

v(0) := .4

.4

 (3)
> 

NULL
> 

s(0) := 0.6e-1

0.6e-1

 (4)
> 

e[0] := .24

.24

 (5)
> 

i[0] := .17

.17

 (6)
> 

r[0] := .13

.13

 (7)
> 

c := 0.4e-1

0.4e-1

 (8)
> 

f := .4

.4

 (9)
> 

beta := .2

.2

 (10)
> 

epsilon := .8

.8

 (11)
> 

theta[1] := .1

.1

 (12)
> 

theta[2] := .3

.3

 (13)
> 

alpha := .9

.9

 (14)
> 

rho := .7

.7

 (15)
> 

eta := .99

.99

 (16)
> 

delta := .3

.3

 (17)
> 

a := 0.4e-1

0.4e-1

 (18)
> 

phi := 1
> 

``
> 

``

``


 

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