m=8
for i=1:m-1
for b=1:m
for c=1:m
F(b)=[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix(:,i+1) - t_val *[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix1* matrix(:,i+1) - delta +[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix1 * matrix(:,i+1) + delta * [E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix1 * matrix(:,i+1) + Gamma
F(c)=[E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix(:,i+1) - [E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)] * matrix1 * matrix(:,i+1) - delta* [E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix1 * matrix(:,i+1)- Gamma + t_val *[E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)] * matrix1* matrix(:,i+1) + Gamma
iam solving this using matlab iam getting only E(1),E(2),E(3),E(4),E(5),E(6),E(9),E(10),E(11),E(12),E(13),E(14) these values the remaining values(E(7),E(8),E(15),E(16)) are not solved. Matlab gives initial guess instead of solution
Solving a nonlinear equation using MATLAB involves using chemical or optimization algorithms to find solutions to the equation or system of equations. Here are some general steps to proceed:
Equation definition: Write an equation or system of equations according to the mathematical representation in MATLAB. It is necessary to have a clear concept of the structure and type of equation you want to solve.
Choose a solution algorithm: Choose a reasonable algorithm to solve the non-linear equation. Some popular algorithms include Newton-Raphson, Bisection, Secant method, and Gradient descent:
fsolve: Use the Newton-Raphson algorithm to solve non-linear equations.
bisep or bisect: Bisection algorithm, applied to single variable equations.
fzero: Integrates algorithms for solving single-variable equations, including Bisection, Regula Falsi, and Newtons's Method.
Sorting initial points: If you have known sorting points, you can use them as initial points for the solving algorithm. For example, with fsolve you can use the following call to use the sort point as [x_guess; y_guess]:
copy
sol = fsolve(@(xy) fun(xy(:)), [x_guess; y_guess]);
Check the results: After executing the algorithm, check the results to ensure they are exact or close enough solutions to your requirements. In case the results are incorrect, you can change the starting point or algorithm to improve the results.
Additionally, you can also use toolboxes such as Optimization Toolbox or Global Optimization Toolbox to solve more complex problems.
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