Solving differential equations with Fourier series and Evolution Strategies
Chaquet, José M. y Carmona, Enrique J. . (2012) Solving differential equations with Fourier series and Evolution Strategies. Applied Soft Computing 12(9), 3051–3062 (2012)
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A novel mesh-free approach for solving differential equations based on Evolution Strategies (ESs) is presented. Any structure is assumed in the equations making the process general and suitable for linear and nonlinear ordinary and partial differential equations (ODEs and PDEs), as well as systems of ordinary differential equations (SODEs). Candidate solutions are expressed as partial sums of Fourier series. Taking advantage of the decreasing absolute value of the harmonic coefficients with the harmonic order, several ES steps are performed. Harmonic coefficients are taken into account one by one starting with the lower order ones. Experimental results are reported on several problems extracted from the literature to illustrate the potential of the proposed approach. Two cases (an initial value problem and a boundary condition problem) have been solved using numerical methods and a quantitative comparative is performed. In terms of accuracy and storing requirements the proposed approach outperforms the numerical algorithm.
This is an Accepted Manuscript of an article published by Elsevier in "Applied Soft Computing, 12(9), 3051–3062 (2012)", available at: http://dx.doi.org/10.1016/j.asoc.2012.05.014
Notas adicionales
Este es el manuscrito aceptado del artículo publicado por Elsevier en "Applied Soft Computing, 12(9), 3051–3062 (2012)", disponible en línea: http://dx.doi.org/10.1016/j.asoc.2012.05.014
