Lie group and RK4 for solving nonlinear first order ODEs

Computer Algebra Solving of First Order ODEs Using Symmetry Methods

A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1 order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1 order ODEsolver and routines for, among other things: the explicit determination of the coefficients of the infinitesimal symmetry generator; the construction of the most general invariant 1 order ODE under given symmetries...

Telescoping Decomposition Method for Solving First Order Nonlinear Differential Equations

The Telescoping Decomposition Method (TDM) is a new iterative method to obtain numerical and analytical solutions for first order nonlinear differential equations. The method is a modified form of the well-known Adomian Decomposition Method (ADM) where the Adomian polynomials have not to be calculating. The (TDM) is easier to apply and offers better accuracy than the (ADM). Also, it can be appl...

A method for solving first order fuzzy differential equation

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...

Variable Step Block Backward Differentiation Formula for Solving First Order Stiff ODEs

block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of th...