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On weighted Adams-Bashforth rules
One class of the linear multistep methods for solving the Cauchy problems of the form , , contains Adams-Bashforth rules of the form , where 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\u27+B(x)y=G(x,y), quad y(x_0)=y_0,]where and are two polynomials determining the well-known classical weight functions in the theory of orthogonal polynomials. Some numerical examples are also included