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Problem-With-Boundary-Condition-At-Infin...

salauayobami 25 Maple
ode homework dsolve
April 29 2022
0 3

I am having a problem in evaluating a fluid flow problem at a boundary that includes infinity using a semi-analytic method Adomian Decomposition Method.

Find the attached code. Thanks in advance.

Plotting styles in Maple...

salauayobami 25 Maple
parameters numeric differential-equations
December 18 2021
1 0

EYRING POWELL FINITE DIFFERENCE ...

salauayobami 25 Maple
ode syntax 2dmath
December 16 2021
2 8

finite difference method 

> 

restart
> 

with(ODETools)
> 

unprotect('gamma')
> 

unprotect(GAMMA)
> 

Digits := 3
> 

M := M; delta := delta; Ec := Ec; Pr := Pr; A := A; GAMMA := GAMMA; gamma := gamma; Q := Q; R := R; S := S; Sc := Sc

M

  

delta

  

Ec

  

Pr

  

A

  

GAMMA

  

gamma

  

Q

  

R

  

S

  

Sc

 (1)
> 

ODE1 := d(1+GAMMA)*(diff(f(eta), eta, eta, eta, eta))-S*(eta*(diff(f(eta), eta, eta, eta))+3*(diff(f(eta), eta, eta))+(diff(f(eta), eta))(diff(f(eta), eta, eta))-f(eta)*(diff(f(eta), eta, eta, eta)))-GAMMA*delta(2*(diff(f(eta), eta, eta))*(diff(f(eta), eta, eta, eta))^2+(diff(f(eta), eta, eta))^2*(diff(f(eta), eta, eta, eta, eta)))-M^2*(diff(f(eta), eta, eta)) = 0

d(1+GAMMA)*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta))-S*(eta*(diff(diff(diff(f(eta), eta), eta), eta))+3*(diff(diff(f(eta), eta), eta))+(diff(f(eta), eta))(diff(diff(f(eta), eta), eta))-f(eta)*(diff(diff(diff(f(eta), eta), eta), eta)))-GAMMA*delta(2*(diff(diff(f(eta), eta), eta))*(diff(diff(diff(f(eta), eta), eta), eta))^2+(diff(diff(f(eta), eta), eta))^2*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)))-M^2*(diff(diff(f(eta), eta), eta)) = 0

 (2)
> 

ODE2 := (1+4*R*(1/3))*(diff(theta(eta), eta, eta))+Pr*S*(f(eta)*(diff(theta(eta), eta))-eta*(diff(theta(eta), eta))+Q*theta(eta)) = 0

(1+(4/3)*R)*(diff(diff(theta(eta), eta), eta))+Pr*S*(f(eta)*(diff(theta(eta), eta))-eta*(diff(theta(eta), eta))+Q*theta(eta)) = 0

 (3)
> 

ODE3 := diff(phi(eta), eta, eta)+Sc*S*(f(eta)*(diff(phi(eta), eta))-eta*(diff(phi(eta), eta)))-Sc*gamma*phi(eta) = 0

diff(diff(phi(eta), eta), eta)+Sc*S*(f(eta)*(diff(phi(eta), eta))-eta*(diff(phi(eta), eta)))-Sc*gamma*phi(eta) = 0

 (4)
> 

bc := f(0) = 0, (D(f))(0)^2 = 0, f(1) = 1, (D(f))(1) = 0, (D(theta))(0) = 0, theta(1) = 1, (D(phi))(0) = 0, phi(1) = 1

f(0) = 0, (D(f))(0)^2 = 0, f(1) = 1, (D(f))(1) = 0, (D(theta))(0) = 0, theta(1) = 1, (D(phi))(0) = 0, phi(1) = 1

 (5)

``

 (6)
> 

parameter := [S = .5, GAMMA = .1, delta = .1, gamma = .1, M = 1, Pr = 1, Ec = .2, Sc = .6, R = 1, Q = 1]

[S = .5, GAMMA = .1, delta = .1, gamma = .1, M = 1, Pr = 1, Ec = .2, Sc = .6, R = 1, Q = 1]

 (7)
> 

SOL := dsolve({bc, subs(parameter, ODE1), subs(parameter, ODE2), subs(parameter, ODE3)}, type = numeric, method = bvp[middefer], output = listprocedure)

Error, (in fproc) unable to store '15.0099999999999998/d(1.1)' when datatype=float[8]

  
> 

Sol := dsolve({bc, subs(parameter, ODE1), subs(parameter, ODE2), subs(parameter, ODE3)}, type = numeric, method = bvp[middefer], output = listprocedure, initmesh = 1024, abserr = 0.1e3)

Error, (in fproc) unable to store '15.0099999999999998/d(1.1)' when datatype=float[8]

  
> 

SOL(1)

SOL(1)

 (8)
> 

NULL
> 

``

Download FDM_EYRING_POWELL.mw

Plotting of a nonlinear differential equ...

salauayobami 25 Maple 2020
ode dsolve nonlinear
December 03 2021
1 3

Plotting of a nonlinear differential equation?

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