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A Galerkin procedure for systems of differential equations

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Abstract

A continuous time and an extrapolated coefficient Crank-Nicolson-Galerkin method are considered for approximating solutions of boundary and initial value problems for a quasi-linear parabolic system of partial differential equations which is coupled to a non-linear system of ordinary differential equations. A priori bounds are derived that reduce the estimation of error to problems in approximation theory. Then approximation theory results yield optimal order rates of convergence for theH 1 (Ω) norm. The extrapolated coefficient method yields linear algebraic equations for strongly non-linear problems.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 78712, Austin, Texas

    J. R. Cannon

  2. Department of Mathematics, Ohio State University Columbus, 43210, Ohio

    R. E. Ewing

Authors
  1. J. R. Cannon
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  2. R. E. Ewing
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Additional information

this research was supported in part by the National Science Foundation Grant No. MCS 75-21317 and Energy-related Postdoctoral Fellowship at the University of Chicago.

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Cannon, J.R., Ewing, R.E. A Galerkin procedure for systems of differential equations. Calcolo 17, 1–23 (1980). https://doi.org/10.1007/BF02575859

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  • DOI: https://doi.org/10.1007/BF02575859

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