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

Daniel X. Guo

doi:10.11948/2013018

2013 Volume 3 Issue 3

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Daniel X. Guo. A SEMI-LAGRANGIAN RUNGE-KUTTA METHOD FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 251-263. doi: 10.11948/2013018

Citation:

Daniel X. Guo. A SEMI-LAGRANGIAN RUNGE-KUTTA METHOD FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 251-263. doi: 10.11948/2013018

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

Daniel X. Guo

Department of Mathematics and Statistics, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28405, US

Abstract

Abstract

In this paper, a Semi-Lagrangian Runge-Kutta method is proposed to compute the numerical solution of time-dependent partial differential equations. The method is based on Lagrangian trajectory or the integration from the departure points to the arrival points (regular nodes). The departure points are traced back from the arrival points along the trajectory of the path. The high order interpolation is needed to compute the approximations of the solutions on the departure points, which most likely are not the regular nodes. On the trajectory of the path, the similar techniques of RungeKutta are applied to the equations to generate the high order Semi-Lagrangian Runge-Kutta method. The numerical examples show that this method works very efficient for the time-dependent partial differential equations.
- Semi-Lagrangian /
- trajectory /
- Runge-Kutta /
- time-dependent partial differential equations
MSC: 76D05;74H15;68W25;65Y20

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References

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