On the analysis and application of a spectral collocation scheme for the nonlinear two-dimensional fractional diffusion equation
Ihteram Ali, Sirajul Haq, Manzoor Hussain, Kottakkaran Sooppy Nisar, Shams Ul Arifeen
Abstract
In this paper, we propose and analyze a novel spectral scheme for the numerical solution of a two-dimensional time-fractional diffusion equation. The proposed scheme approximates the unknown function and its derivatives in space by finite Lucas and Fibonacci polynomial expansion, and time derivative/variable by L1 formula with θ-weighted difference scheme. Error estimates are derived and convergence is proved. Six test problems are then solved to verify the theory numerically. The obtained results confirm the low computational cost and better accuracy than known results in the literature.
Topics & Concepts
MathematicsCollocation (remote sensing)Convergence (economics)Fractional calculusApplied mathematicsSpectral methodNonlinear systemDiffusion equationScheme (mathematics)PolynomialDiffusionVariable (mathematics)Space (punctuation)Mathematical analysisComputer sciencePhysicsService (business)Machine learningQuantum mechanicsEconomyEconomicsThermodynamicsOperating systemEconomic growthFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis