Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method
This paper explores the approximate analytical solution of non-linear Klein-Gordon equations (NKGE) by using multistep modified reduced differential transform method (MMRDTM). Through this proposed strategy, the non-linear term is substituted by associating Adomian polynomials obtained by utilizatio...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
VINCA Institute of Nuclear Sciences
2019-01-01
|
Series: | Thermal Science |
Subjects: | |
Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361900045C.pdf |
id |
doaj-a2e93d550a2a44be9d8d440e35939553 |
---|---|
record_format |
Article |
spelling |
doaj-a2e93d550a2a44be9d8d440e359395532021-01-02T11:50:27ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362019-01-0123Suppl. 131732610.2298/TSCI181015045C0354-98361900045CAnalytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform MethodChe Hussin Che Haziqah0Ismail Ahmad Izani1Kilicman Adem2Azmi Amirah3Universiti Sains Malaysia, School of Mathematical Sciences, USM, Gelugor, Penang, Malaysia + Preparatory Centre of Science and Technology, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu, Sabah, MalaysiaUniversiti Sains Malaysia, School of Mathematical Sciences, USM, Gelugor, Penang, MalaysiaUniversiti Putra Malaysia, Institute for Mathematical Research, Serdang Selangor, MalaysiaUniversiti Sains Malaysia, School of Mathematical Sciences, USM, Gelugor, Penang, MalaysiaThis paper explores the approximate analytical solution of non-linear Klein-Gordon equations (NKGE) by using multistep modified reduced differential transform method (MMRDTM). Through this proposed strategy, the non-linear term is substituted by associating Adomian polynomials obtained by utilization of a multistep approach. The NKGE solutions can be obtained with a reduced number of computed terms. In addition, the approximate solutions converge rapidly in a wide time region. Three examples are provided to illustrate the effectiveness of the proposed method to obtain solutions for the NKGE. Graphical results are shown to represent the behavior of the solution so as to demonstrate the validity and accuracy of the MMRDTM.http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361900045C.pdfAdomian polynomialsmultistep approachNKGEreduced differential transform method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Che Hussin Che Haziqah Ismail Ahmad Izani Kilicman Adem Azmi Amirah |
spellingShingle |
Che Hussin Che Haziqah Ismail Ahmad Izani Kilicman Adem Azmi Amirah Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method Thermal Science Adomian polynomials multistep approach NKGE reduced differential transform method |
author_facet |
Che Hussin Che Haziqah Ismail Ahmad Izani Kilicman Adem Azmi Amirah |
author_sort |
Che Hussin Che Haziqah |
title |
Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method |
title_short |
Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method |
title_full |
Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method |
title_fullStr |
Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method |
title_full_unstemmed |
Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method |
title_sort |
analytical solutions of nonlinear klein-gordon equations using multistep modified reduced differential transform method |
publisher |
VINCA Institute of Nuclear Sciences |
series |
Thermal Science |
issn |
0354-9836 |
publishDate |
2019-01-01 |
description |
This paper explores the approximate analytical solution of non-linear Klein-Gordon equations (NKGE) by using multistep modified reduced differential transform method (MMRDTM). Through this proposed strategy, the non-linear term is substituted by associating Adomian polynomials obtained by utilization of a multistep approach. The NKGE solutions can be obtained with a reduced number of computed terms. In addition, the approximate solutions converge rapidly in a wide time region. Three examples are provided to illustrate the effectiveness of the proposed method to obtain solutions for the NKGE. Graphical results are shown to represent the behavior of the solution so as to demonstrate the validity and accuracy of the MMRDTM. |
topic |
Adomian polynomials multistep approach NKGE reduced differential transform method |
url |
http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361900045C.pdf |
work_keys_str_mv |
AT chehussinchehaziqah analyticalsolutionsofnonlinearkleingordonequationsusingmultistepmodifiedreduceddifferentialtransformmethod AT ismailahmadizani analyticalsolutionsofnonlinearkleingordonequationsusingmultistepmodifiedreduceddifferentialtransformmethod AT kilicmanadem analyticalsolutionsofnonlinearkleingordonequationsusingmultistepmodifiedreduceddifferentialtransformmethod AT azmiamirah analyticalsolutionsofnonlinearkleingordonequationsusingmultistepmodifiedreduceddifferentialtransformmethod |
_version_ |
1724354845148708864 |