I have been working on 50 non linear differential equation with fsolve but it always give me this answer please help how can i solve this problem

I have been working on fins equation and faced non linear eqaution so i have used fsolve command but every time it show this thing

[Torsten]

Why do you use "fsolve" for differential equations ?

"fsolve" is designed to solve nonlinear algebraic equations, "ode45" or "ode15s" are designed to solve differential equations.

[Akasha]

I have apply fdm central scheme so d.e changes in ko 50 non linear algebraic eqaution

[Matt J]

There's nothing in your post to show us that the solution it's giving you is wrong.

[Torsten]

I have apply fdm central scheme so d.e changes in ko 50 non linear algebraic eqaution

But in the title you write that you work on 50 nonlinear differential equations ...

Maybe using a solver for boundary value problems is a better choice than discretizing on your own. Look up "bvp4c" or "bvp5c".

[Akasha]

I will share more details with you tomorrow

Answer 1

[Sulaymon Eshkabilov]

There are a couple of points to consider.

(1) if fsolve() has to be used, then fsolve()'s options need to be set up to perform N number of iterations, e.g.:

% Function handle of the problem to be solved solve
EQNs = @(x) ([x(1)^2 + x(2)^2 - 1;
             exp(x(1)) + x(2) - 2;
             sin(x(1) + x(2)) - x(3);
             cos(x(4)) - x(5)^2;
             log(x(4) + x(5)) - 3]);
% Number of Iterations to perform:
N = 10;
% Set the options of fsolve(): 
OPTs = optimoptions('fsolve', 'MaxIter', N, 'Display','iter');
% Initial Guess Solutions:
X_guess = [1; 1; 1; 1; 1];

% Solve the system of equations
[Solution, Fval] = fsolve(EQNs, X_guess, OPTs)

                                             Norm of      First-order   Trust-region
 Iteration  Func-count     ||f(x)||^2           step       optimality         radius
     0          6             9.49361                            6.71              1
     1         12             5.13647              1            0.859              1
     2         13             5.13647            2.5            0.859            2.5
     3         19             4.89156          0.625            0.304          0.625
     4         20             4.89156          0.625            0.304          0.625
     5         26             4.80326        0.15625            0.196          0.156
     6         32             4.73656        0.15625            0.176          0.156
     7         38             4.67347       0.390625            0.339          0.391
     8         39             4.67347       0.390625            0.339          0.391
     9         45             4.59588      0.0976562            0.278         0.0977
    10         51             4.46835       0.244141             0.36          0.244

Solver stopped prematurely.

fsolve stopped because it exceeded the iteration limit,
options.MaxIterations = 1.000000e+01.

Solution = 5×1

0.0865 0.9929 0.8962 2.9799 0.3517

Fval = 5×1

-0.0066 0.0833 -0.0145 -1.1107 -1.7966

disp('Found solution: ')

Found solution: 

disp(Solution)

    0.0865
    0.9929
    0.8962
    2.9799
    0.3517

(2) lsqnonlin() is good to solve large size nonlinear problems:

% Function handle of the problem to be solved solve
EQNs = @(x) ([x(1)^2 + x(2)^2 - 1;
             exp(x(1)) + x(2) - 2;
             sin(x(1) + x(2)) - x(3);
             cos(x(4)) - x(5)^2;
             log(x(4) + x(5)) - 3]);
% Initial Guess Solutions:
X_guess = [1; 1; 1; 1; 1];
% Set Lower bound:
LB = [0; 0; 0;  0; 0; ];
% Set Lower bound:
UB = [10; 10; 10;  10; 10; ];
% Max Number of Iterations:
N = 10;
% Options set up:
OPT2 = optimoptions('lsqnonlin', 'MaxIterations', N, 'Display','iter');
% Use lsqnonlin() to solve EQNs:
[SOLUTION, FVAL] = lsqnonlin(EQNs, X_guess, LB, UB, OPT2)

                                            Norm of      First-order 
 Iteration  Func-count      Resnorm            step       optimality
     0          6           9.49361                              6.9
     1         12           6.03506        0.815721             4.66      
     2         18           4.72506         1.09483             9.26      
     3         24           2.02104        0.273708             2.82      
     4         30           1.36831        0.547416             1.89      
     5         36          0.931038        0.424434            0.582      
     6         42          0.894717        0.499556             2.09      
     7         48          0.819859        0.124889           0.0684      
     8         54          0.819032        0.249778            0.238      
     9         60          0.816667       0.0624444            0.247      
    10         66          0.814251       0.0624444          0.00533      
    11         72          0.812845        0.137778           0.0771      

Solver stopped prematurely.

lsqnonlin stopped because it exceeded the iteration limit,
options.MaxIterations = 1.000000e+01.

SOLUTION = 5×1

0.0280 0.9944 0.8535 7.7640 0.4494

FVAL = 0.8128

[Akasha]

[Akasha]

this is my function file

[Akasha]

[Akasha]

this is my using fsolve command file in which i call my function

[Akasha]

[Akasha]

this is the output which matlab gives me i dont know how to solve it fully please help me