Explicit solutions of Cauchy problems for degenerate hyperbolic equations with Transmutations methods
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Allameh Tabataba'i University Press
2022-07-01
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| Series: | Mathematics and Modeling in Finance |
| Subjects: | |
| Online Access: | https://jmmf.atu.ac.ir/article_14574_21dd15d702dd977b586960751ec33e85.pdf |
| Summary: | 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. |
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| ISSN: | 2783-0578 2783-056X |