Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data

Muhammad Asif Gondal, Inayatur Rehman, Asima Razzaque

Abstract

The paper presents error bounds for the second order exponential Runge-Kutta method for parabolic abstract linear time-dependent differential equations incorporating non-smooth initial data. As an example for this particular type of problems, the paper presents a spatial discretization of a partial integro-differential equation arising in financial mathematics, where non-smooth initial conditions occur in option pricing models. For this example, numerical studies of the convergence rate are given

Keywords

Exponential integrators, Runge–Kutta methods, Integro-differential equations.

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