Hybrid Finite Integration Method for Solving Partial Differential Equations

In this paper, a Hybrid Finite Integration Method (HFIM), modified based on the research of P.H. Wen et al. (Wen et al. 2015), is presented to solve partial differential equations. The method requires the integral matrix, induced by the combination of the trapezoidal rule and Simpson's rule to produce the integral matrix. This paper also confirms the advantage of using HFIM that only one integral matrix is required to solve the n-th order differential equation. The integral matrix is straightforward to implement and not complicated. Moreover, in order to demonstrate the HFIM's accuracy and efficiency, we illustrate numerical examples and compared the results with the finite difference method and the traditional FIM.