A New Parallelized Computation Method of HASC-N Difference Scheme for Inhomogeneous Time Fractional Fisher Equation

Abstract

The fractional Fisher equation has a wide range of applications in many engineering fields. The rapid numerical methods for fractional Fisher equation have momentous scientific meaning and engineering applied value. A parallelized computation method for inhomogeneous time-fractional Fisher equation (TFFE) is proposed. The main idea is to construct the hybrid alternating segment Crank-Nicolson (HASC-N) difference scheme based on alternating segment difference technology, using the classical explicit scheme and classical implicit scheme combined with Crank-Nicolson (C-N) scheme. The unique existence, unconditional stability and convergence are proved theoretically. Numerical tests show that the HASC-N difference scheme is unconditionally stable. The HASC-N difference scheme converges to O(τ2−α+h2) under strong regularity and O(τα+h2) under weak regularity of fractional derivative discontinuity. The HASC-N difference scheme has high precision and distinct parallel computing characteristics, which is efficient for solving inhomogeneous TFFE.