Exact solution to partial differential equations based on Lie symmetries by operator exponential rule
DOI:
https://doi.org/10.35819/remat2024v10i2id6913Keywords:
Lie symmetries, exponential of operators, partial differential equation, exact solutionAbstract
In this work it is presented the exponential method of operators is presented, which consists of a technique for solving partial differential equations (PDE) that involve linear operators with the characteristic of invariance. Starting from the idea based on Lie symmetries, we propose a representation of a solution in terms of an exponential of a linear operator, which is obtained through the expansion of the exponential in a series of powers and the use of an approximation technique to deal with each term in the series. This technique involves decomposing the operator into a sum of two or more simple operators, which can be exactly solved and, therefore, without the need to talk about analysis of convergence, stability or errors involved in the approximation of the differential operators involved. Five first-order partial differential equations are solved, verifying the exact nature of the solutions found, in addition to their illustration in graphic form.
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