New numerical methods for Burgers' equation based on semi-Lagrangian and modified equation approaches

• Autores: Jin Wang, Anita Layton
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 6, 2010, págs. 645-657
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.03.007
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• Resumen

  • In this paper, we develop a class of semi-Lagrangian finite difference schemes which are derived by a new algorithm based on the modified equation technique; and we apply those methods to the Burgers' equation. We show that the overall accuracy of the proposed semi-Lagrangian schemes depends on two factors: one is the global truncation error which can be obtained by the modified equation analysis, the other is a generic feature of semi-Lagrangian methods which characterizes their non-monotonic dependence on the time stepsize. The analytical results are confirmed by numerical tests.