基于变步长L1格式的时间分数阶Fisher方程的数值解法-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Numerical Solution of the Time-Fractional Fisher′s Equation Based on the Variable-Step L1 Scheme

Author(s):: ZHU Xiaojuan; CHEN Xuejuan; CHEN Ao; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: time fractional Fisher′s equation; variable-step L1 scheme; second order center difference; stability; convergence

摘要:: 考虑非线性时间分数阶Fisher方程的数值解法,对其时间分数阶导数应用变步长L1格式进行离散,空间二阶导数应用二阶中心差分进行离散,并利用离散互补卷积(discrete complementary convolution,DCC)核技术证明了该格式在L2范数下是无条件稳定的,且在时间方向具有2-α阶收敛精度,空间方向具有2阶收敛精度。最后通过数值算例验证了所构造格式的可行性和有效性。

Abstract:: This article investigates the numerical solution of the nonlinear time fractional Fisher equation.The time fractional derivative is discretized by the variable step size L1 scheme,and the space second derivative is discretized by the second order central difference scheme.By using the technique of the discrete complementary convolution (DCC) kernel,we present that this scheme is unconditionally stable under the L2 norm,and the 2-α order convergence accuracy in time and the second order convergence accuracy in space can be achieved.Finally,the feasibility and effectiveness of the proposed scheme are validated through numerical examples.