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

Authors

  • Muhammad Asif Gondal Dhofar University
  • Inayatur Rehman
  • Asima Razzaque

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3423

Keywords:

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

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

Author Biography

  • Muhammad Asif Gondal, Dhofar University

    Professor of Mathematics,

    Department of Mathematics and Sciences

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Published

2019-07-25

Issue

Vol. 12 No. 3: (July 2019)

Section

Nonlinear Analysis

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data. (2019). European Journal of Pure and Applied Mathematics, 12(3), 1215-1230. https://doi.org/10.29020/nybg.ejpam.v12i3.3423