Element Free Galerkin Method For Solving Differential Equations With Control

Element free Galerkin method (EFGM) is a new numerical method emerged inrecent years. It is one of the Element free method variety, but application of EFGMis the most widely used. Moving least squares used to construct the shapefunctions while equations obtained from the energy functional variational form, andthe Lagrange multipliers meet with displacement boundary conditions to get thenumerical solution of differential equations. Advantage of this approach is obviousby simplifying the data processing to improve the speed of calculation. We can alsosolve some of the problem that the finite element method can be not solved. Specificwork is as follows:First, as EFGM Method in Differential Equations in its infancy, thedevelopment is still not perfect. When selecting different interpolation scheme,different weight function, different trial function and different local sub-domains, itwill generate different effects. The solution may be biased, so the solution is nothigh precision. In order to get better accuracy, starting from the weight function, thepaper researches how to generate a Gaussian function coefficient matrix freeGalerkin method. For the differential equations, in the course of using EFGMapproximation solution method to solve differential equations, and start from theweight function, free Galerkin method in combination moving least squareapproximation method, to approximate the solution of differential equationsconsidered truncated Gaussian function as a weight function.Secondly, from a variety of classes starting weight function, considercombining two kinds of weighting function. The main study will combine splinefunction and truncated Gaussian function as law EFGM a weight function to solutedifferential equations. Using least squares method to generate the shape function anduse Lagrange multiplier to generates a new integral equation. Finally, the numericalsolution can be obtained.Finally, the two methods described above were prepared MATLAB program and get algorithm, with specific data results show that the method is effective andpractical in this article.