Analysis of linear and nonlinear stiff problems using the RK-Butcher algorithm

S. Sekar

Mathematical Problems in Engineering, 2006, vol. 2006, 1-15

Abstract:

I present a numerical solution of linear and nonlinear stiffproblems using the RK-Butcher algorithm. The obtained discretesolutions using the RK-Butcher algorithm are found to be veryaccurate and are compared with the exact solutions of the linearand nonlinear stiff problems and also with the Runge-Kutta methodbased on arithmetic mean (RKAM). A topic of stability for theRK-Butcher algorithm is discussed in detail. Error graphs fordiscrete and exact solutions are presented in a graphical form toshow the efficiency of the RK-Butcher algorithm. The resultsobtained show that RK-Butcher algorithm is more useful for solvinglinear and nonlinear stiff problems and the solution can beobtained for any length of time.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:039246

DOI: 10.1155/MPE/2006/39246

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