Abstract
This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.
Highlights
D ifferential equation can represent most systems or phenomena undergoing change. They are quotidian in science, engineering and biology as well as in economics, social science, health and business [1]
Systems described by differential equations are so complex, or the systems they represent are so large that a purely analytical treatment may not be tractable
Adomian decomposition method (ADM) solves nonlinear operator equations for any analytic nonlinearity providing an computable, readily verifiable and rapidly convergent sequence of analytic approximate solutions. Since it was first presented in the 1980’s, Adomian decomposition method has led to several modifications on the method made by various researchers in an attempt to improve the accuracy or expand the application of the original method [23]
Summary
D ifferential equation can represent most systems or phenomena undergoing change. They are quotidian in science, engineering and biology as well as in economics, social science, health and business [1]. Depending on the nature of the system at hand, differential equations may be linear, pseudo-linear or nonlinear. Systems described by differential equations are so complex, or the systems they represent are so large that a purely analytical treatment may not be tractable. A simple example is Newton’s second law of motion–the relationship between the displacement x and the time t of an object under the force F is given by the differential equation d2x(t) m dt2 = F(x(t)), which constrains the motion of a particle of constant mass m. F is a function of the position x(t) of the particle at time t
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