## Solve nonlinear system of equations ...

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...

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...

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);

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

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...

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?...

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...

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...

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.

School of Mathematical Sciences
Peking University, Beijing, China

## iterative method for nonlinear equation...

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)

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

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

 (1)

 (2)

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

thanks...

## ODE non linear first order...

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...

Hy Prof.

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))

## how i can pdsolve this nonlinear equations...

thanksoffcenter2.mw

 (1)

 (2)

 (3)

#####################################

 (4)

at x=

 (5)

 (6)

 (7)

############################################

at x=0

 (8)

 (9)

################################################

at t=0 for x= [0,La]

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

######################################################

at t=0 for x= [0,La)

 (17)

 (18)

###################################################

at t=0 for x=La

 (19)

 (20)

## HELP : got unable to store error...

Hi everyone!

I have a problem solving the nonlinear ode (as attached below). I got this error ---> Error, (in fproc) unable to store '-1.32352941215398+(-0.441176470717993e-1, -0.)' when datatype=float[8]

1) Could someone please explain to me what does the unable store .... error means?

and i will be grateful if you could help me finding the solution out. Thanks in advance

## Solving a nonlinear system of 4 equations using sh...

Dear All,

I have a problem solving the attached nonlinear system of equations using shooting method.
I will be grateful if you could help me finding the solutions out.

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta)).gp(eta)+2.*g(eta)*fp(eta)+2.*N2.N3.(m(eta).np(eta)-n(eta).mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m.(m(eta)+(eta-2.*f(eta)).mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m.(2.*n(eta)+(eta-2.*f(eta)).np(eta)+2.*N2/N3.m(eta).gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta)).fppp(eta)-2.*N2.N2.m(eta).(diff(mp(eta), eta)))};
blt := 1.0; IC := {f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2};
BC := {f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC, FNS, [alpha1 = 1.425, alpha2 = .425, beta1 = -1.31, beta2 = 1.00, beta3 = 1.29]);
Error, (in isolate) cannot isolate for a function when it appears with different arguments
p := odeplot(S, [eta, fp(eta)], 0 .. 15);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p);
Error, (in plots:-display) expecting plot structure but received: p
p2 := odeplot(S, [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p2);
Error, (in plots:-display) expecting plot structure but received: p2

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