Page 46 - programme book

DE-001
Approximate Analytical Solutions of Second-Order Nonlinear Telegraph
Equations

Che Haziqah Che Hussin 1, b) , Arif Mandangan 2,a) , Amirah Azmin 3, c) and Adem Kilicman 4, d)

1 Preparatory Centre for Science and Technology, Universiti Malaysia Sabah,
Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia.
2 Faculty of Science and Natural Resources, Universiti Malaysia Sabah,
Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia.
3 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
4 Institute for Mathematical Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.

a) Corresponding author: arifman@ums.edu.my
b)
haziqah@ums.edu.my
c) amirahazmi@usm.my
d) akilic@upm.edu.my

Abstract. Multistep Modified Reduced Differential Transform Method (MMRDTM) is proposed and
implemented in this study to solve nonlinear telegraph equations (NLTEs). This method involves
replacement of the nonlinear term in NLTEs with corresponding Adomian polynomials prior to
adopting the multi-step approach. As a result, we offer alternatives for solving NLTEs in a simpler and
less difficult manner. Furthermore, the solutions can be approximated more accurately over a longer
period of time. In order to demonstrate the capability and accuracy of the MMRDTM, we considered
several NLTEs and presented the features of the solutions in graphs and tabular forms. From the results
of this study, the MMRDTM was found to provide highly accurate solutions or exact solutions for
these types of equations.

Keywords: Adomian polynomials, modified approach, multistep approach, Reduced Differential
Transform Method, nonlinear Telegraph equations

44