Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method
Mine Aylin Bayrak, Ali Demir, Ebru Ozbılge
Abstract
In this paper, we propose an efficient Chebyshev collocation scheme to solve diffusion problem including time fractional diffusion equation considering the fractional derivative in the Liouville-Caputo sense. By making use of shifted Chebyshev polynomial series and their orthogonality properties, the problem is reduced to the system of fractional ordinary differential equations which can be solved by residual power series method (RPSM) with the help of the given scheme and boundary conditions. The numerical examples shows that the method is reliable and effective to construct the numerical solution of fractional diffusion equation.
Topics & Concepts
MathematicsMethod of mean weighted residualsChebyshev equationChebyshev polynomialsFractional calculusOrthogonalityPower seriesOrthogonal collocationCollocation methodMathematical analysisCollocation (remote sensing)Chebyshev filterChebyshev nodesResidualApplied mathematicsSeries (stratigraphy)Diffusion equationOrdinary differential equationDifferential equationOrthogonal polynomialsFinite element methodGalerkin methodAlgorithmClassical orthogonal polynomialsComputer scienceGeometryService (business)PaleontologyThermodynamicsBiologyEconomicsPhysicsMachine learningEconomyFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations