backward difference

Numerical analysis on chaos attractors using a backward difference formulation

The chaos attractor is a system of ordinary differential equations which is known for having chaotic solutions for certain parameter values and an initial condition.  Research conducted in the current work establishes a backward difference algorithm to study these chaos attractors.  Different types of chaos mapping, namely the Lorenz chaos, 'sandwich' chaos and 'horseshoe' chaos will be analyzed.  Compared to other numerical methods, the proposed backward difference algorithm will show to be an efficient tool for analyzing solutions for the chaos attractors.

Variable order step size method for solving orbital problems with periodic solutions

Existing variable order step size numerical techniques for solving a system of higher-order ordinary differential equations (ODEs)  requires direct calculating the integration coefficients at each step change.  In this study, a variable order step size is presented for direct solving higher-order orbital equations.  The proposed algorithm calculates the integration coefficients only once at the beginning and, if necessary, once at the end.  The accuracy of the numerical approximation is validated with well-known orbital differential equations.  To reduce computational costs, we obtain the r

A backward difference formulation for analyzing the dynamics of capital stocks

The current study provides a numerical method that is derived in a backward difference formulation for ordinary differential equations.  The proposed method employs a constant step size algorithm of order 12.  The backward difference formulation serves as a competitive algorithm for solving ordinary differential equations.  In the current study, the backward difference method is used to analyze the dynamics of capital stocks in terms of depreciation rate for the capital–labor ratio.  Results provided in this study will validate the accuracy of the backward difference algorithm hence proving