Numerical scheme for solving system of fractional partial differential equations with Volterra‐type integral term through two‐dimensional block‐pulse functions

Abstract

In the current study, an approximate scheme is established for solving the fractional partial differential equations (FPDEs) with Volterra integral terms via two‐dimensional block‐pulse functions (2D‐BPFs). According to the definitions and properties of 2D‐BPFs, the original problem is transformed into a system of linear algebra equations. By dispersing the unknown variables for these algebraic equations, the numerical solutions can be obtained. Besides, the proof of the convergence of this system is given. Finally, several numerical experiments are presented to test the feasibility and effectiveness of the proposed method.

Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation

“…Though we only consider the ROEFSECN method of the 2D nonstationary Stokes problem, our method could be generalize to more complex partial differential equations and the actual engineering problems, such as hydrodynamic equations [1][2][3], fractional partial differential equations [36][37][38], unsaturated soil water flow problems [39,40], and nonlinear viscoelastic equations with delay terms [41]. Hence, the method in this paper possesses far-ranging applied prospect.…”

Approximate Solution of System of Multi-Term Fractional Mixed Volterra-Fredholm Integro-Differential Equations by BPFs

“…One of the numerical methods that have been used effectively for solving integral equations and FIDEs is BPFs method [24][25][26][27][28][29][30][31][32][33]35]. The BPFs method is a method with low cost of setting up the equations without using any projection methods.…”