Original scientific paper

On weighted Adams-Bashforth rules

Mohammad Masjed-Jamei ; Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Gradimir Milovanović ; Serbian Academy of Sciences and Arts, Beograd, Serbia
Amir Hossein Salehi Shayegan ; Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

Abstract

One class of the linear multistep methods for solving the Cauchy problems of the form $ y'=F(x,y) $, $ y(x_{0})=y_{0} $, contains Adams-Bashforth rules of the form $y_{n+1}=y_{n}+h\sum_{i=0}^{k-1} B_i^{(k)} F(x_{n-i},y_{n-i})$, where $\{ B_i^{(k)}\} _{i = 0}^{k - 1}$ are fixed numbers. In this paper, we propose an idea for weighted type of Adams-Bashforth rules for solving the Cauchy problem for singular differential equations,\[A(x)y'+B(x)y=G(x,y), \quad y(x_0)=y_0,\]where $A$ and $B$ are two polynomials determining the well-known classical weight functions in the theory of orthogonal polynomials. Some numerical examples are also included.

Keywords

weighted Adams-Bashforth rule; ordinary differential equation; linear multistep method; weight function

Hrčak ID:

192137

URI

https://hrcak.srce.hr/192137

Publication date:

30.5.2018.

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