Solving system of linear Integro-differential equations by finite integration method with shifted Chebyshev polynomials

Abstract

In this thesis, we modify the finite integration method by using the shifted Chebyshev polynomial (FIM-SCP). The major tool of our FIM-SCP is the shifted Chebyshev integration matrix. It is constructed in order to be a matrix representation for integrating over interpolated points which are generated by the zeros of shifted Chebyshev polynomial of a certain degree. The efficiently numerical algorithms are then created by the modified FIM-SCP for seeking approximate solutions of a system of stiff linear ordinary differential equations, a system of linear Volterra integro-differential equations, and a system of linear Fredholm integro-differential equations under some given boundary conditions. Furthermore, our three proposed algorithms are examined the performance via the diversified numerical experiments. The comparisons of their analytical solutions or approximate solutions obtained by our proposed algorithms with other methods are also illustrated through the average absolute error. They provide that our numerical algorithms achieve a significantly accurate improvement.