On factorization and solution of multidimensional linear partial differential equations
S.P. Tsarev
TL;DR
This paper introduces a generalized method for solving certain multidimensional second-order linear PDEs, extending classical Laplace transformation techniques to higher dimensions based on historical ideas from Dini.
Contribution
It presents a novel approach that generalizes classical methods for solving multidimensional second-order linear PDEs, enabling closed-form solutions.
Findings
Provides a systematic method for solving specific multidimensional PDEs.
Extends classical Laplace transformation techniques to higher dimensions.
Offers closed-form solutions for certain classes of PDEs.
Abstract
We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations of second-order hyperbolic equations in the plane and is based on an idea given by Ulisse Dini in 1902.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic and Geometric Analysis · Numerical methods for differential equations