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

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Akasha 2024-1-13

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https://ww2.mathworks.cn/matlabcentral/answers/2069546-i-have-been-working-on-50-non-linear-differential-equation-with-fsolve-but-it-always-give-me-this-a

编辑： Akasha 2024-1-14

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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

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Torsten 2024-1-13

编辑：Torsten 2024-1-13

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 2024-1-13

I will share more details with you tomorrow

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Answer 1

Sulaymon Eshkabilov 2024-1-14

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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