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Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods

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Abstract

This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Inonu University, 44280, Malatya, Turkey

    BILGE INAN & AHMET REFIK BAHADIR

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  1. BILGE INAN
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  2. AHMET REFIK BAHADIR
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Correspondence to BILGE INAN.

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INAN, B., BAHADIR, A.R. Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods. Pramana - J Phys 81, 547–556 (2013). https://doi.org/10.1007/s12043-013-0599-z

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  • DOI: https://doi.org/10.1007/s12043-013-0599-z

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