On a multiwavelet spectral element method for integral equation of a generalized Cauchy problem

Abstract In this paper we deal with construction and analysis of a multiwavelet spectral element scheme for generalized Cauchy type problem Caputo fractional derivative. Numerical schemes problems, often suffer from the draw-back spurious oscillations. A common remedy is to render an equivalent integral equation. For problem, corresponding equation nonlinear Volterra type. investigate wellposedness convergence stabilizing a, one-dimensional case (in [ , b ] or [0, 1]), problem. Based on multiwavelets, construct approximation procedure operator that yields linear system equations sparse coefficient matrix. setting, choosing appropriate threshold, number non-zero coefficients in substantially reduced. severe obstacle lack continuous derivatives vicinity inflow/ starting boundary point. We overcome issue through separating J (mesh)-dependent, small, neighborhood (or origin) interval, where only take $$L_2$$ L 2 -norm. The estimate part relies Chebyshev polynomials, viz. As reported by Richardson( interpolation functions endpoint singularities via exponential double-exponential transforms, Oxford University, UK, 2012) decreases, almost, exponentially raising . At remaining domain solution sufficiently regular derive desired optimal error bound. such modified analyze its wellposedness, efficiency accuracy. robustness proposed confirmed implementing numerical examples.