A SEMI-LAGRANGIAN RUNGE-KUTTA METHOD FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS | Zendy

Daniel X. Guo | Zendy

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A SEMI-LAGRANGIAN RUNGE-KUTTA METHOD FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

Author(s) -

Daniel X. Guo

Publication year - 2013

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2013018

Subject(s) - mathematics , runge–kutta methods , trajectory , partial differential equation , mathematical analysis , interpolation (computer graphics) , lagrangian , path (computing) , ordinary differential equation , differential equation , computer science , classical mechanics , physics , motion (physics) , astronomy , programming language

In this paper, a Semi-Lagrangian Runge-Kutta method is proposed to com-pute the numerical solution of time-dependent partial di®erential equations.The method is based on Lagrangian trajectory or the integration from the de-parture points to the arrival points (regular nodes). The departure points aretraced back from the arrival points along the trajectory of the path. The highorder interpolation is needed to compute the approximations of the solutionson the departure points, which most likely are not the regular nodes. On thetrajectory of the path, the similar techniques of Runge-Kutta are applied to theequations to generate the high order Semi-Lagrangian Runge-Kutta method.The numerical examples show that this method works very effient for thetime-dependent partial di®erential equations.

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