Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel
Ahmed Gamal Atta, Y. H. Youssri
Abstract
Abstract This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up a new Hilbert space that satisfies the initial and boundary conditions. The new spectral collocation approach is applied to obtain precise numerical approximation using new basis functions based on shifted first-kind Chebyshev polynomials (SCP1K). Furthermore, we support our study by a careful error analysis of the suggested shifted first-kind Chebyshev expansion. The results show that the new approach is very accurate and effective.
Topics & Concepts
MathematicsChebyshev polynomialsCollocation (remote sensing)Chebyshev equationChebyshev filterKernel (algebra)Hilbert spaceChebyshev iterationNonlinear systemMathematical analysisCollocation methodApplied mathematicsSpectral methodDifferential equationOrthogonal polynomialsClassical orthogonal polynomialsPure mathematicsOrdinary differential equationComputer scienceQuantum mechanicsPhysicsMachine learningFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials