How to create new script which contains nonlinear algebraic equation including integral?

I want to get variables which are A, lamda2, lamda4, however, it doesn't come up with method about coding.

Trapezoidal rule with repeating code should be used to get those variables, I guess, but I have no idea about it all.

Please let me know how to start or outline code.

Answer 1

[Surya Talluri]

I understand that you wants to implement the integrals in MATLAB. You can use Symbolic Math Toolbox to implement it

syms A lamda2 lamda4 alpha beta gamma P2(beta) P4(beta) f(alpha,beta,gamma) F(beta)
int1 = int(int(int(f(alpha,beta,gamma)*sin(beta),beta, 0,pi),alpha ,0,2*pi),gamma,0,2*pi) == 1

int2 = int(int(int(P2(cos(beta))*F(beta)*sin(beta),beta, 0,pi),alpha ,0,2*pi),gamma,0,2*pi) == 0.530

int3 = int(int(int(P4(cos(beta))*F(beta)*sin(beta),beta, 0,pi),alpha ,0,2*pi),gamma,0,2*pi) == 0.348

eqn = f(alpha,beta,gamma) == F(beta);
F(beta) = A*exp(-lamda2*P2(cos(beta))+lamda4*P4(cos(beta)))

since P2(cos(beta)) and P4(cos(beta)) are functions of beta, we need more information about them to solve the integrals.

You can refer to following documentation for further understanding of the toolbox:

• int - https://in.mathworks.com/help/symbolic/int.html
• solve - https://in.mathworks.com/help/symbolic/solve.html