Simulation of imprecise ordinary differential equations using evolutionary algorithms
SAC '00 Proceedings of the 2000 ACM symposium on Applied computing - Volume 1
Applied Mathematics and Computation
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Evolutionary Modeling of Systems of Ordinary Differential Equations with Genetic Programming
Genetic Programming and Evolvable Machines
A heuristic particle swarm optimizer for optimization of pin connected structures
Computers and Structures
ISTASC'06 Proceedings of the 6th WSEAS International Conference on Systems Theory & Scientific Computation
Numerical solution of nonlinear Volterra-Fredholm integro-differential equations
Computers & Mathematics with Applications
A heuristic particle swarm optimization method for truss structures with discrete variables
Computers and Structures
Introduction to Genetic Algorithms
Introduction to Genetic Algorithms
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A general algorithm is presented to approximately solve a great variety of linear and nonlinear ordinary differential equations (ODEs) independent of their form, order, and given conditions. The ODEs are formulated as optimization problem. Some basic fundamentals from different areas of mathematics are coupled with each other to effectively cope with the propounded problem. The Fourier series expansion, calculus of variation, and particle swarm optimization (PSO) are employed in the formulation of the problem. Both boundary value problems (BVPs) and initial value problems (IVPs) are treated in the same way. Boundary and initial conditions are both modeled as constraints of the optimization problem. The constraints are imposed through the penalty function strategy. The penalty function in cooperation with weighted-residual functional constitutes fitness function which is central concept in evolutionary algorithms. The robust metaheuristic optimization technique of the PSO is employed to find the solution of the extended variational problem. Finally, illustrative examples demonstrate practicality and efficiency of the presented algorithm as well as its wide operational domain.