Local meshless collocation scheme for numerical simulation of space fractional PDE
Mehnaz Shakeel, Muhammad Nawaz Khan, Imtiaz Ahmad, Hijaz Ahmad, Nantapat Jarasthitikulchai, Weerawat Sudsutad
Abstract
In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The fractional derivatives of radial basis functions are evaluated by Caputo and Riemann-Liouville definitions. Local radial basis functions are applied to get stable and accurate solution the problem. Accuracy of the method is assessed by using double mesh procedure. Numerical solutions are presented for different fractional orders to show the effect of introducing fractionality.
Topics & Concepts
Radial basis functionCollocation (remote sensing)Fractional calculusSpace (punctuation)Regularized meshless methodBasis (linear algebra)Collocation methodMathematicsScheme (mathematics)Work (physics)Applied mathematicsBasis functionTerm (time)Mathematical analysisComputer scienceSingular boundary methodFinite element methodPhysicsDifferential equationGeometryBoundary element methodOrdinary differential equationQuantum mechanicsThermodynamicsOperating systemMachine learningArtificial neural networkFractional Differential Equations SolutionsNumerical methods in engineeringIterative Methods for Nonlinear Equations