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

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.