SOLUTION OF THE MIXED PROBLEM FOR THE ONE-DIMENSIONAL WAVE EQUATION WITH THE USE OF THE CHARACTERISTIC PARALLELOGRAM METHOD
Abstract
This article is aimed at constructing a solution to the first mixed problem for the one-dimensional wave equation in the form convenient for numerical implementation with the help of the characteristic parallelogram. The derivation of the formula for numerical solution is based on the representation of the classical solution of the considered problem. This problem is formulated as follows. The one-dimensional wave equation is given in the half-strip on the plane of the two independent variables. Cauchy conditions assigned on the basis of the half-strip are related to the equation. Values of the sought solution are set by the given functions on the lateral half-line side of the area. The parallelogram method can be extended to other equations and problems.
About the Author
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Academician, D. Sc. (Physics and Mathematics), Professor
References
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