Open AccessSin-Cos-Taylor-Like method for solving stiff ordinary diffrential equations
Author(s) -
Rokiah Rozita Ahmad,
Norsuzila Ya’acob
Publication year - 2014
Publication title -
malaysian journal of fundamental and applied sciences
Language(s) - English
Resource type - Journals
ISSN - 2289-599X
DOI - 10.11113/mjfas.v1n1.13
Subject(s) - runge–kutta methods , l stability , mathematics , backward differentiation formula , ordinary differential equation , polynomial , function (biology) , property (philosophy) , linear multistep method , computation , taylor series , stability (learning theory) , work (physics) , exponential function , order (exchange) , differential equation , mathematical analysis , computer science , differential algebraic equation , algorithm , mechanical engineering , philosophy , epistemology , finance , evolutionary biology , machine learning , engineering , economics , biology
This paper discusses the derivation of an explicit Sin-Cos-Taylor-Like method for solving stiff ordinary differential equations, which is a formulation of the combination of a polynomial and the exponential function. This new method requires extra work to evaluate a number of differentiations of the function involved. However, the result shows smaller errors when compared to the results from the explicit classical fourth-order Runge-Kutta (RK4) and the Adam-Bashforth-Moulton (ABM) methods. Implicit methods could work well for stiff problems but have certain drawbacks especially when discussing about the cost. Although extra work is required, this explicit method has its own advantages. Besides providing excellent results, the cost of computation using this explicit method is much cheaper than the implicit methods. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge-Kutta method is not adequate for the solution of stiff problems. As a result, we find that this explicit method is of order-6, which has been developed, and proved to be both A-stable and L-stable.