Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Evolution strategies –A comprehensive introduction
Natural Computing: an international journal
Solving differential equations with genetic programming
Genetic Programming and Evolvable Machines
Genetic Programming and Evolvable Machines
Unsupervised adaptive neural-fuzzy inference system for solving differential equations
Applied Soft Computing
Analytic solutions to differential equations under graph-based genetic programming
EuroGP'10 Proceedings of the 13th European conference on Genetic Programming
IEEE Transactions on Evolutionary Computation
Genetic Programming Approaches for Solving Elliptic Partial Differential Equations
IEEE Transactions on Evolutionary Computation
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks
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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.