## apply while loop inside other while loop...

iam trying to apply newton method on non liner system but i have a problem for apply while loop inside other while loop

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## Fsolve, 20 ecuations, 20 unknows...

Hi, i wonder if there is a way to solve this 20×20 equations system for maple. Im trying fsolve but it doesn't work. aceitoso

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## how to solve this system?...

updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));

restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);

g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));

1, c1
2       2    2   2
16 y  + 16 x , s1  s2
2
8 x, c1 s2
2      2    2
2 y  + 2 x , s1  c2
2 x, c1 c2
3            2
2 x  - 2 x + 2 y  x, s2 c2
2
1, c2
2 x, s3
2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system

but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.

originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));

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

#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]});

## How to draw this graph?...

A system of algebraic equation

in terms of x, y, z

how draw 3 different circles to show the range of possible values for x, y and z respectively?

it may not be a circle

It may be 3 bounded area graph to show the range of x , y , z respectively

updated

like the graph in many examples in

algebraic and geometric ideas in the theory of discrete optimization

bound area have color

## 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

## Why Maple does not solve this simple system of dif...

Hi,

Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

## Finding the eigenvalues...

Hello guys,

I have some system of differential equations,

How can i find  eigenvalues of this system?

If i have solution

res := evalf(dsolve(sys union ics, convert(x, list), type = numeric, method = rkf45))

and

sol := evalf(dsolve(sys union ics, convert(x, list), method = laplace))

AnSolution.mw

Thanks!

## solve a system of 3 equations...

I want to get solutions of this system ,can anyone help me ?solutions.mw

## How can I get the Transfer Function from an Equati...

Hi, I am new in Maple. If I have an electric network as in the figure, I want to get the Transfer Function V2(s)/Vi(s) from this equation system:

Vi=R1.I1+V1

Vi=R2.I2+V2

I1-I2=C1.dV1/dt

I2=C2.dV2/dt

Which are the commands that I may write to get this?? Before hand, Thanks by your answers!

## Problem to fined the solution of system of nonline...

Dear

Hope you will be fine. My file takes to much time to solve the system of nonlinear algebraic equations for Iterations=8. please solve my problem I will be waiting for positive response.

Error_graph.mw

## How can I solve Linear ODEs system using matrix me...

$$\textbf{x}' = \begin{bmatrix} -4 & -2 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}+\begin{bmatrix} -t \\ -2t-1 \end{bmatrix},\textbf{x}(0)=\begin{bmatrix} 3 \\ -5 \end{bmatrix}$$

As I know firstly, when the matrix is denoted by $A$, we must compute $e^{At}$ by diagonalizing $A$: if $A=PDP^{-1}$ for a diagonal $D$ then $e^{At} = P e^{Dt} P^{-1}$ where $e^{Dt}$ is a diagonal matrix with $(e^{Dt})_{ii} = e^{D_{ii} t}$...

How can I write The Maple code? maple.stackexchange)

restart: with(LinearAlgebra):

A := Matrix(2,2,[-4,-2,3,1]);

....

## Problem to solve system of linear PDEs with BSc an...

Hello

Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response.

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## 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

## 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.