Exponential Convolution Quadrature for Nonlinear Subdiffusion Equations with Nonsmooth Initial Data
Buyang Li, Shu Ma
Abstract
An exponential type of convolution quadrature is proposed as a time-stepping method for the nonlinear subdiffusion equation with bounded measurable initial data. The method combines contour integral representation of the solution, quadrature approximation of contour integrals, multistep exponential integrators for ordinary differential equations, and locally refined stepsizes to resolve the initial singularity. The proposed $k$-step exponential convolution quadrature can have $k$th-order convergence for bounded measurable solutions of the nonlinear subdiffusion equation based on natural regularity of the solution with bounded measurable initial data.
Topics & Concepts
MathematicsQuadrature (astronomy)Mathematical analysisBounded functionNonlinear systemExponential functionSingularityConvolution (computer science)Gauss–Kronrod quadrature formulaTanh-sinh quadratureNyström methodApplied mathematicsIntegral equationArtificial neural networkComputer scienceQuantum mechanicsPhysicsElectrical engineeringEngineeringMachine learningFractional Differential Equations SolutionsNumerical methods for differential equationsDifferential Equations and Numerical Methods