## THERMAL SCIENCE

International Scientific Journal

### A COMPUTATIONAL METHOD FOR SOLVING DIFFERENTIAL EQUATIONS WITH QUADRATIC NONLINEARITY BY USING BERNOULLI POLYNOMIALS

**ABSTRACT**

In this paper, a matrix method is developed to solve quadratic nonlinear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. And 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 nonlinear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds.

**KEYWORDS**

PAPER SUBMITTED: 2018-11-28

PAPER REVISED: 2018-12-26

PAPER ACCEPTED: 2019-01-15

PUBLISHED ONLINE: 2019-03-09

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 1**, PAGES [S275 - S283]

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