Hello Gaurav,
To solve the given equation using a modified 2nd order Newton-Raphson method in MATLAB, you can refer to the following steps:
- Use numerical methods to evaluate the integral on the left-hand side. MATLAB provides the integral function for this purpose, which is suitable for handling complex integrands.
- Initialize the parameters ‘a’, ‘b’, and ‘c’. These initializations can be arbitrary but should be based on the context of the problem.
- The modified 2nd order version involves using both the first and second derivatives (gradient and Hessian) to update the parameters.
- Gradient (First Derivative): Compute the gradient of the integral with respect to each parameter. This involves differentiating the integrand with respect to ‘a’, ‘b’, and ‘c’.
- Hessian (Second Derivative): Compute the Hessian matrix, which contains the second derivatives of the integral with respect to the parameters.
- Update the parameters iteratively using the Newton-Raphson update rule:
delta = -hessian \ gradient;
a = a + delta(1);
b = b + delta(2);
c = c + delta(3);
Now, continue iterating until the change in parameters is below a certain tolerance level or a maximum number of iterations is reached. This ensures that the solution converges to the desired accuracy.
Please refer to the documentation of integral which can be used during implementation: https://www.mathworks.com/help/matlab/ref/integral.html
I hope it helps you query!
