On numerical simulations of time fractional Phi-four equation using Caputo derivative - Kamran, Mohsin; Majeed, Abdul; Li, Jing (Computational & applied mathematics, 2021)
The fractional model which played an essential role in nuclear and particle physics used to describe the nuclear element interaction is the Phi-four model. This manuscript aims to scrutinize the new numerical solution of the nonlinear time fractional Phi-four equation subject to nonhomogeneous initial-boundary conditions by means of cubic-B-spline collocation method (CBSCM). The main advantage of cubic B-spline method over existing techniques is that it efficiently provides a piecewise-continuous, closed form solution and it is simpler and easy to apply to many problems involving partial differential equations. In this approach the fractional differential equation is converted into system of equations. The non-integer derivative " α " is considered in Caputo sense. The discretization of Caputo derivative is done using L 1 formula, while B-spline basis functions are used for the interpolation of spatial derivative. The applicability of the proposed scheme is examined on two test problems. The influence of different parameters is studied and captured graphically and numerically. The proposed scheme is proved to be unconditionally stable. Moreover, the error norms are computed to quantify the accuracy.