## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL SOLUTIONS OF A CLASS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS IN HERMITE SERIES

**ABSTRACT**

The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ordinary differential equation with nonlinear terms under mixed conditions. The method we used is a matrix method based on collocation points together with truncated Hermite series and reduces the solution of equation to solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Hermite coefficients. In addition, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing result in literature.

**KEYWORDS**

PAPER SUBMITTED: 2018-12-15

PAPER REVISED: 2018-12-30

PAPER ACCEPTED: 2019-01-10

PUBLISHED ONLINE: 2019-03-09

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 1**, PAGES [S339 - S351]

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