Meshfree collocation method for implicit time integration of ODEs

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method. © 2011 World Scientific Publishing Company.