Different advanced mathematics are used to integral, solve system of equations and solve differential equations. A summary is given below:

• Numerical integration methods: trapezoidal integration, Gaussian quadrature, Monte Carlo, Simpson and adaptive methods (C++)
• Solution of the algebraic system of equations: Gaussian elimination, Gauss-Seidel, Jacobi, GMRES, conjugate gradient and multigrid methods (C++)
• Perturbation approaches: Adomian decomposition, homotopy analysis, and variational iteration methods (Matlab)