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Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods | ||
| Journal of Mathematics and Modeling in Finance | ||
| مقاله 12، دوره 2، شماره 1، مهر 2022، صفحه 209-247 اصل مقاله (282.51 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2022.14574 | ||
| نویسندگان | ||
| Mahdieh Aminian Shahrokhabadi1؛ Hossein Azari* 2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. | ||
| 2Shahid Beheshti University | ||
| چکیده | ||
| This article's primary goal is to compute an explicit transmutation-based solution to a degenerate hyperbolic equation of second order in terms of time. To reduce a new problem to a problem that has already been solved, or at the very least to a smaller problem, is a standard mathematics strategy known as the transmutations method. similar to utilizing heat equations to solve wave equations. Using transmutation methods, we solve this problem using the well-known Kolmogorov equation. We present the solution of wave equations using transmutation methods and show that it is equivalent to the solution obtained by applying the Fourier transform in order to support our methodology. | ||
| کلیدواژهها | ||
| Degenerate Partial Differential Equations؛ Transmutation Methods؛ Kolmogorov Equation؛ Inverse Laplace Transform؛ Laplace Transform | ||
| مراجع | ||
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