A constructive algorithm using Chebyshev spectral collocation is proposed for computing trustworthy approximate solutions of linear and weakly nonlinear delayed partial differential equations or initial boundary value problems, with continuous and bounded coefficients. The boundary conditions are assumed to be Dirichlet. The solution of linear problems is obtained at Chebyshev grid points in space and a given interval of time. The algorithm is then extended to systems with weak nonlinearities using perturbation series, which yields nonhomogeneous initial boundary value problems without delay. The proposed methodology is illustrated using examples of linear and weakly nonlinear heat and wave equations with bounded continuous space-time varying coefficients.
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April 2012
Research Papers
Solutions of Delayed Partial Differential Equations With Space-Time Varying Coefficients
Venkatesh Deshmukh
e-mail: venkatesh.deshmukh@villanova.edu
Venkatesh Deshmukh
Department of Mechanical Engineering
, 800 Lancaster Avenue, Villanova
, PA 19085
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Venkatesh Deshmukh
Department of Mechanical Engineering
, 800 Lancaster Avenue, Villanova
, PA 19085e-mail: venkatesh.deshmukh@villanova.edu
J. Comput. Nonlinear Dynam. Apr 2012, 7(2): 021002 (7 pages)
Published Online: December 22, 2011
Article history
Received:
February 26, 2011
Revised:
September 2, 2011
Online:
December 22, 2011
Published:
December 22, 2011
Citation
Deshmukh, V. (December 22, 2011). "Solutions of Delayed Partial Differential Equations With Space-Time Varying Coefficients." ASME. J. Comput. Nonlinear Dynam. April 2012; 7(2): 021002. https://doi.org/10.1115/1.4005081
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