NUMERICAL SOLUTION OF VARIABLE-ORDER TIME FRACTIONAL WEAKLY SINGULAR PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ERROR ESTIMATION
Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi
Abstract
In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-differential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate.
Topics & Concepts
MathematicsLegendre polynomialsAlgebraic equationVariable (mathematics)Applied mathematicsCollocation methodKernel (algebra)Laguerre polynomialsTransformation (genetics)Collocation (remote sensing)Matrix (chemical analysis)Mathematical analysisDifferential equationOrdinary differential equationNonlinear systemComputer sciencePure mathematicsPhysicsBiochemistryQuantum mechanicsChemistryMaterials scienceGeneComposite materialMachine learningFractional Differential Equations SolutionsNumerical methods for differential equationsIterative Methods for Nonlinear Equations