## suggestion on faster solving set of nonlinear ODEs...

Asked by:

#first_question :how can i solve set of nonlinear ODEs,faster or using any packages ?
#second_question :what can be some boundary conditions for this type of nonlinear ODEs? how many BCs are required for this set of nonlinear ODEs? ( to use numeric solution)

 > restart:with(DEtools):with(DifferentialAlgebra):
 > eq[1]:=diff(N(r),r\$2)+2/r*diff(N(r),r)+diff(phi(r),r)/phi(r)*diff(N(r),r)-mu^2/(32*phi(r))*N(r);
 (1)
 > eq[2]:=diff(phi(r),r\$2)+2/r*diff(phi(r),r)-1/2*diff(phi(r),r)^2/phi(r)-8*diff(N(r),r)^2/(omega*(1-2*G*M/r))*phi(r);
 (2)
 > dsolve({eq[1],eq[2]});

Download nonlinear_ODE.mw

## method = lsode doesnot work on Coupled IVP...

Asked by:

the Initial value problem is well defined but i could not find solution of the problem. A number of method have been used but all are useless. How to obtained graph of the all equations. Also can we find the value of R (radius) where P is zero.coupled_IVP.mw

## finding standard error of the cofficents in nonlin...

Asked by:

hello i was wondering is it possible to find the standard error of the coefficents in the NonlinearFit function within the statistical package? or in any other package for that matter?

does someone have angorithme that can find it?

i've searched around the internet and it does not seem like maple employs this function at all?

hope someone can help:)

## Solve nonlinear system of equations ...

Asked by:

Hi

I have a nonlinear PDEs, solved using finite difference in the square

I get the following nonlinear system of equation. Is there any idea how correct the code and display the solution.

I will appreciate any help in this question.

restart;
n:=100;
h:=1/(n+1);

# Boundary condition

for j from 0 by 1  to n+1 do
u[0, j] = 0;
u[n+1, j] = 0;
u[j, 0] = 0;
u[j, n+1] = 0 ;
end do;
## Loop for interior point in the square
for i from 1 by 1 to  n do
for j from 1 by 1 to  n do
(u[i+1, j]-u[i, j])*(u[i+1, j]-2*u[i, j]+u[i-1, j])+h*(u[i, j+1]-2*u[i, j]+u[i, j-1]) = 0;
end do;
end do;

How can I solve this system of equations with unknown u[i,j], where i,j=1,..,n

Many thanks for any help

## How do I solve a nonlinear equation with sin and s...

Asked by:

How do I?
I'm very new in Maple, just I wanna learn a lot but i don't know where to start.
I have to find x,y, Tl, Th and Ti

Maybe we can help me at least a litle bit :D
thanks

## How to solve a non linear first degree partial equ...

Asked by:

Hello,

I have been trying to solve a simple nonlinear equation. Im interested in the solution per say rather than the plot but when I browsed about the commands to use, this came up. I tried it in my case and it is giving me the following errors:

 > restart;

 > with(plots);
 (1)
 > eq5:=C*sqrt(y(x)*((diff(y(x),x))^2+1))-y(x)=0;
 (2)
 > C:=1;
 (3)
 > bcs:=y(-1)=1, y(1)=1;
 (4)
 > dsys:={eq5,bcs};
 (5)
 > dsol:=dsolve(dsys, numeric); odeplot(dsol,[x,y(x)],0..1,color=red,axes=box);

Download ode.mw

## Solving a non linear system of PDE...

Asked by:

I want to solve the following non linear PDE

SS := [diff(u(x, y, t), t)-0.625e-1*(diff(u(x, y, t), x, x)+diff(u(x, y, t), y, y))-6*(diff(u(x, y, t)*(diff(v(x, y, t), x)), x)+diff(u(x, y, t)*(diff(v(x, y, t), y)), y)) - 2*(u(x, y, t))(1-u(x, y, t))=0, diff(v(x, y, t), t)-(diff(v(x, y, t), x, x))-(diff(v(x, y, t), y, y))+16*v(x, y, t) -u(x, y, t)=0]

when i use the command

sol := pdsolve(SS, [u, v], singsol = false)

maple give the error message

Error, (in pdsolve) found the independent variables {t, x, y} also present in the names of the functions of the system []

## How can I solve a set of equations that one of the...

Asked by:

I solve a set of equations in this way and I have three set of answers ,but I don`t know wich one is true.

and I have another question ,how can I assume v[0] like a constant?

alpha[2]:= 2.727272728*10^5: alpha[4]:= 3738.685337: alpha[6]:= -30.18675539: alpha[7] := -4.116375735*10^6: alpha[8] := 1.859504132*10^10: alpha[9]:= 2.489142857*10^(-12):

l10:=(alpha[7]*v[0]^2+1)*gamma[i*n]^4+(-alpha[4]*beta[n]^2+alpha[8]*v[0]^2-alpha[9])*gamma[i*n]^2+(2*I)*gamma[i*n]*alpha[2]*beta[n]*v[0]+(2*I)*gamma[i*n]^3*alpha[6]*beta[n]*v[0]-beta[n]^2 = 0:

l11 := subs(i = 1, l10);

l12 := subs(i = 2, l10);

l13 := subs(i = 3, l10);

l14 := subs(i = 4, l10);

l15 := (exp(I*(gamma[n]+gamma[2*n]))+exp(I*(gamma[3*n]+gamma[4*n])))*(gamma[3*n]^2-gamma[4*n]^2)*(gamma[n]^2-gamma[2*n]^2)+(exp(I*(gamma[n]+gamma[4*n]))+exp(I*(gamma[2*n]+gamma[3*n])))*(gamma[2*n]^2-gamma[3*n]^2)*(gamma[n]^2-gamma[4*n]^2)+(exp(I*(gamma[2*n]+gamma[4*n]))+exp(I*(gamma[n]+gamma[3*n])))*(gamma[2*n]^2-gamma[4*n]^2)*(-gamma[n]^2+gamma[3*n]^2) = 0;

l1 := combine(expand(evalc(l15)), trig):

l2 := combine(expand(evalc(Re(l15))), trig):

l3 := combine(expand(evalc(Im(l15))), trig): v[0] := 1; 1

fsolve({l1, l11, l12, l13, l14}, {beta[n], gamma[n], gamma[2*n], gamma[3*n], gamma[4*n]}):

fsolve({l11, l12, l13, l14, l2}):

solve({l11, l12, l13, l14, l3}):

thanks

Reyhaneh

## How can I solve this symbolic nonlinear system?...

Asked by:

I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:

wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.

I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!

PS:the mw file is given here.

A_symbolic_nonlinear_system.mw

## How to solve 12 nonlinear equations with 12 variab...

Asked by:

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw

## Solution of system of nonlinear algebraic equation...

Asked by:

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response.

Help_in_Newton.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

## iterative method for nonlinear equation...

Asked by:

hy

i have to develop a code i which i have system of nonlinear equation

i have to generate the matrix of that nonlinear equation then i want to do or apply any method say newton method and make a loop which help us to find a solution using some tolerance

at the end i get a result in form of a table which give nth matrix then value of function matrix at nth value then error i-e xn-x(n-1)

thanx in advance

## error for dsolve differential equation.......

Asked by:

hi..i have a problem for solving this nonlinear differential equationerror.mw

 (1)

 (2)

############################################################CHANGE OF VARIABLE:::           x=y*L

Download error.mw

please help me

thanks...

## ODE non linear first order...

Asked by:

Dear all,

I would like to solve the following non linear ODE with Maple, but I am no able. I do not know if it is possible, beccause it is nolinear.

I really appreciate any advice or help. This is the equation:

y'(x) - (Q - x*p0*(exp(alpha-beta*y(x)))/(1+exp(alpha-beta*y(x))))^2=0

thanks a lot

## Nonlinear Coupled PDE...

Asked by:

Hy Prof.

Please help me or guide me to get idea to solve Nonlinear coupled PDEwith MAPLE.Dr.Sam Dao could please help me as I saw your YOUTUBE lecturer which very helpful to me and please give some idea about my topic.

pde[1] := diff(u(x, t), t)-D(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-E(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thanks in advance and answer is highly appricaited

 1 2 3 4 5 6 7 Page 1 of 7
﻿