A linear k-step method for solving ordinary differential equations

Abstract

The field of differential equations, no doubt, plays a vital role in the applications of mathematics to scientific and engineering problems. A considerable number of the important physical laws of the universe, more often than not, is expressed in differential equation form. Therefore, the solution of a differential equation implies the solution of the physical problem it represents. Although a multitude of families of approximate numerical methods for solving differential equations exists, for acceptability a numerical method must exhibit convergence; more so, for it to be effective, it must converge rapidly. In this paper, we construct a numerical method of optimal order from the family of linear k-step methods