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Iterative Algorithms for Numerical Solution of Differential Equations with Linearly Transformed Argument

Keywords:

Ya. Yu. Konovalov


Atomic functions are widely applied in different brunches of science and technology. Then construction of effective numerical algorithms for computation atomic function is actual problem. Atomic functions are not analytic and Taylor polynomials are not applicable to their computation. Usually computation of atomic functions is based on Fourier series. In given work iterative approach to computation of compactly supported solutions of differential equations with linearly transformed argument is considered. It makes possible to reduce solution of such equations to simple iterative algorithm which doesn’t require computation of trigonometric and other special functions. Approach is applicable to computation of atomic functions which are compactly supported solutions of differential equations with linearly transformed argument too. Procedure of construction numerical methods for solving such equations is presented. Examples of application of algorithms to computation of atomic functions and solving of more general equations are demonstrated.
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