Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm
TL;DR: In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values.
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Abstract: In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.
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Citations
Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm
TL;DR: The numerical results show that the proposed continuous genetic algorithm is a robust and accurate procedure for solving systems of second-order boundary value problems and the obtained accuracy for the solutions using CGA is much better than the results obtained using some modern methods.
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Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm
TL;DR: A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch's and Bratu's problems by replacing each of the second derivatives by an appropriate difference quotient approximation.
A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method
TL;DR: In this paper, a new analytic method is applied to singular initial-value Lane-Emden type problems, and the effectiveness and performance of the method is studied, which obtains a Taylor expansion of the solution, and when the solution is polynomial, their method reproduces the exact solution.
Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion
TL;DR: In this article , a two-dimensional cross-mode hyperchaotic map based on logistic and sine maps (2D-CLSS) is presented, which combines permutation and diffusion to alter the location and the value of the pixels.
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Solution of Inverse Kinematics Problem using Genetic Algorithms
TL;DR: The superiority of the continuous GA is seen in that it will alway s provide smooth and faster solutions as compared with the co nventional GA.
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References
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David E. Goldberg,William Shakespeare +1 more
- 01 Jan 2002
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