Author(s)

R.A. Walentyriski

Abstract

This paper presents the application of the refined least squares method. The refinement makes it possible to solve problems with not only boundary, but also initial and non-continuous conditions. Mathematica is used to develop algorithms and carry out computations. It enables us to extend fields of approximate analytical method applications and allow them to be regarded as computer ones. Mathematica makes it possible to solve unstable and ill-conditioned tasks which are too difficult for numerical methods. 1 Introduction The problem of approximate solution of boundary value problems with Ma- thematica was already considered by Barrere & Carmasol [1, 2]. They ap- plied the Galerkin method. The least squares method is a well known method in mathematics. It is used to approximate data sets or functions with other functions or to approxima

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