A computational method for solving differential equations with quadratic non-linearity by using bernoulli polynomials
No Thumbnail Available
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Abstract
In this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. Both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds. © 2019 Society of Thermal Engineers of Serbia.
Description
Keywords
Computation theory , Differential equations , Error analysis , Matrix algebra , Polynomials , Absolute error , Approximate solution , Bernoulli polynomials , Function values , Matrix forms , Matrix methods , Non-linear equations , Nonlinear differential equation , Quadratic nonlinearities , Residual functions , Numerical methods