Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 75-83.

Numerical solution for nonlocal Sobolev-type differential equations

Shruti A. Dubey

We present a numerical approximate solution to Sobolev-type differential equation subject to nonlocal initial boundary conditions. A Laplace transform method is described for the solution of considered equation. Following Laplace transform of the original problem, an appropriate method of solving differential equations is used to solve the resultant time-independent modified equation and solution is inverted numerically back into the time domain. Numerical results are provided to show the accuracy of the proposed method.

Published September 25, 2010.
Math Subject Classifications: 35L65, 65M06, 65M12.
Key Words: Sobolev-type differential equations; Laplace transform; numerical inversion; nonlocal conditions.

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Shruti A. Dubey
Laboratoire d'Analyse et d'Architecture des Systemes du CNRS
(LAAS-CNRS), Toulouse, France
email: shrurkd@gmail.com

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