Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 5; pp. 6054 - 6076
• Main Authors: Hadhoud, Adel R., Rageh, Abdulqawi A. M., Agarwal, Praveen
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.03.2023
• Subjects: Boundary conditions; Caputo derivative; Differential equations; Diffusion; fractional differential equations; Gauss–Lobatto quadrature; Numerical methods; Polynomials; Reaction-diffusion equations; shifted Legendre polynomials; space–time fractional coupled reaction–diffusion equations; Thermal expansion
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.8891

This paper proposes the shifted Legendre Gauss–Lobatto collocation (SL‐GLC) scheme to solve two‐dimensional space‐fractional coupled reaction–diffusion equations (SFCRDEs). The proposed method is implemented by expressing the function and its spatial fractional derivatives as a finite expansion of shifted Legendre polynomials. Then the expansion coefficients are determined by reducing the SFCRDEs with their initial and boundary conditions to a system of ordinary differential equations for these coefficients. Subsequently, we applied the proposed method to discretize the temporal and spatial variables to convert the two‐dimensional spacetime fractional coupled reaction–diffusion equations (STFCRDEs) to a system of algebraic equations. Some results regarding the error estimation are obtained. Several examples are discussed to validate the capability and efficiency of the proposed scheme.