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

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How to Cite

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

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