Intertwining Laplace Transformations of Linear Partial Differential Equations
Elena I. Ganzha
TL;DR
This paper introduces a comprehensive generalization of Laplace transformations for linear partial differential operators of any order in multiple variables, unifying previous methods and providing an explicit construction algorithm.
Contribution
It presents a complete algorithm for intertwining Laplace transformations applicable to arbitrary-order LPDOs in R^n, expanding the scope of differential transformations.
Findings
Unified framework for differential transformations of LPDOs
Complete algorithm for constructing ILT in R^n
Identification of operator classes suitable for ILT
Abstract
We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of this transformation (intertwining Laplace transformation, ILT). We give a complete algorithm of construction of ILT and describe the classes of operators in R^n suitable for this transformation. Keywords: Integration of linear partial differential equations, Laplace transformation, differential transformation
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Numerical methods for differential equations