Application Of Numerical Methods Based On Artificial Glowworm Optimization Algorithm

With the rapid development of computer and calculation method, almost all disciplines are to quantitative and precision, thus result in a series of computational subject branch, such as computational physics, computational chemistry, computational biology, computational geology and computational meteorology. Numerical method of computational mathematics is the bridge and tool for solving the calculation problem. Numerical method is a method of studying and solving the numerical approximate solution in mathematics problems, and it is short for calculation method. All kinds of calculation methods are used in scientific research and engineering technology. For example, aerospace, geological prospecting, automobile manufacture, design of Bridges, weather forecast and Chinese characters typeface design have used calculation methods. Calculation objects of calculation method are the mathematical problems of calculus, linear algebra and ordinary differential equations. Main contents include interpolation method and fitting, numerical integration, numerical differentiation, the direct method and the iteration method of solving the system of linear equation group, non-linear equation solution, computation of matrix eigenvalues problem, numerical solution of ordinary differential equations. In traditional numerical methods there are many problems. For example, traditional nonlinear equations methods are difficult to choose initial values and need to restrict the forms of equations and equations must be continuously differentiable, traditional eigenvalues methods have larger store capacity, slower calculating speed, lower accuracy and slow convergence speed, traditional numerical integral methods are very difficult to obtain high accuracy and low complexity, traditional unconstrained optimization methods are difficult to obtain the global optimal solution and so on. In the article we use GSO of the swarm intelligence bionic optimization algorithm to study the related questions of traditional numerical computational methods.The main task of this article is using the characteristics of GSO, such as rapid convergence, global convergence and high accuracy, to solve problems of traditional numerical methods. The proposed numerical methods based on the GSO here mainly include solving nonlinear equations, solving eigenvalues, numerical integral and function constrained optimization problems and so on, which offer a new method for the numerical computation.