Solving the Cauchy Problem for a Two-Dimensional Difference Equation at a Point Using Computer Algebra Methods
| Autor: | Marina S. Apanovich, Alexander P. Lyapin, Konstantin V. Shadrin |
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| Rok vydání: | 2021 |
| Předmět: |
Constant coefficients
Polynomial Differential equation MathematicsofComputing_NUMERICALANALYSIS 020207 software engineering 0102 computer and information sciences 02 engineering and technology Basis (universal algebra) Symbolic computation 01 natural sciences Matrix (mathematics) 010201 computation theory & mathematics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0202 electrical engineering electronic engineering information engineering Initial value problem Applied mathematics Point (geometry) Software Mathematics |
| Zdroj: | Programming and Computer Software. 47:1-5 |
| ISSN: | 1608-3261 0361-7688 |
| DOI: | 10.1134/s0361768821010023 |
| Popis: | An algorithm for finding the solution to the Cauchy problem for a two-dimensional difference equation with constant coefficients at a point using computer algebra is described. In the one-dimensional case, solving the Cauchy problem is easy; however, already in the two-dimensional case the number of unknowns rapidly increases at each step. To automate the process of computing the solution to the Cauchy problem for a two-dimensional difference equation with constant coefficients at a given point, an algorithm in MATLAB is developed in which the input data are the matrix of coefficients obtained on the basis of the structure of the two-dimensional polynomial difference equation, coordinates of the points that specify the structure and the size of the matrix of initial data, and the matrix of the initial data. The algorithm produces the solution to the Cauchy problem for the given two-dimensional difference equation at the given point. |
| Databáze: | OpenAIRE |
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