Analytical solutions of differential equations based on genetic meta-heuristic algorithm and ant colony optimization

Subject Areas : Statistics

Nasser Mikaeilvand ¹ , Akram Javadi ² , Hassan Hosseinzadeh ³

1 - Department of Mathematics, Islamic Azad University, Ardabil Branch, Ardabil, Iran.
2 - Department of Mathematics, Islamic Azad University, Ardabil Branch, Ardabil, Iran.
3 - Department of Mathematics, Islamic Azad University, Ardabil Branch, Ardabil, Iran.

Received: 2019-03-04 Accepted : 2019-10-25 Published : 2020-12-21

Keywords: معادلات دیفرانسیل معمولی, معادلات دیفرانسیل با مشتقات جزئی, برنامه ریزی ترکیبی مورچگان و ژنتیک, مینیمم سازی خطای وابسته,

Abstract :

Many issues are expressed in terms of various applied sciences such as physics, chemistry, and economics, which are concerned with the examination of variations of one or more variables, by differential equations. The prediction of climate, quantum mechanics, wave propagation and dynamics of the stock market is some of these examples, whose quick and accurate solution will have tremendous effects on human life, and therefore several methods have been proposed for solving differential equations.The main objective of this study was to investigate the applicability of the antler colony genetic algorithm to the production of experimental solutions and improve them to produce numerical analytic-numerical solutions of various types of ordinary differential equations. An antler colony optimization algorithm (ACO) has an appropriate algorithm with high convergence accuracy and speed for finding approximate solutions for solving optimization problems using probability function dependent on the amount of residual effect of anti-movement. Genetic algorithm is also an optimization method based on mutated and intersect operators with a wide search area that prevents the algorithm from trapping in the local response. The combination of these two algorithms creates an algorithm with maximum efficiency. Examining various examples in the final section of the article will highlight the speed and accuracy of the proposed method.

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