Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i3.3423Keywords:
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
Downloads
Published
Issue
Section
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.