Explicit green approach (ExGA) for solving partial differential equations in mechanics
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This work presents the formulation and implementation of the solution to partial differential equation systems through the Explicit Green Approach (ExGA). This method uses the Laplace Transform to obtain the solution in the frequency domain and, then, through inverse transform, it makes it posible to explicitly obtain the value that solves the partial differential equation. The versatility of this method in the reduction of computer resources for solving type 2 and 1 linear problems can be observed. Four numerical examples for the heat and elasticity transfer equation are offered. Results show the accuracy of this method, which can use time differentials which are higher to those used in classic time integration algorithms with a solution which is closer to an order algorithm.
Differential equations, continuum mechanics, heat-transmission, elasticityEcuaciones diferenciales, mecánica continua, transmisión del calor, elasticidad
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