Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

被引:86
作者
Ahmad, Hijaz [1 ]
Khan, Tufail A. [1 ]
Stanimirovic, Predrag S. [2 ]
Chu, Yu-Ming [3 ,4 ]
Ahmad, Imtiaz [5 ]
机构
[1] Univ Engn & Technol, Dept Basic Sci, Peshawar, Pakistan
[2] Univ Nis, Fac Sci & Math, Visegradska 33, Nish 18000, Serbia
[3] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[4] Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China
[5] Univ Swabi, Dept Math, Swabi, Khyber Pakhtunk, Pakistan
基金
中国国家自然科学基金;
关键词
AUXILIARY PARAMETER; NUMERICAL-SOLUTION; GALERKIN METHOD; WAVE-LIKE; EQUATIONS; SCHEME; KIND;
D O I
10.1155/2020/8841718
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.
引用
收藏
页数:14
相关论文
共 48 条
[1]   Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems [J].
Ahmad H. ;
Khan T.A. .
Noise and Vibration Worldwide, 2020, 51 (1-2) :12-20
[2]  
Ahmad H., 2018, Nonlinear Science Letters A, V9, P27
[3]  
Ahmad H., 2020, J OCEAN ENG SCI
[4]   Modified Variational Iteration Technique for the Numerical Solution of Fifth Order KdV-type Equations [J].
Ahmad, Hijaz ;
Khan, Tufail A. ;
Stanimirovic, Predrag S. ;
Ahmad, Imtiaz .
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2020, 6 :1220-1227
[5]   Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm [J].
Ahmad, Hijaz ;
Seadawy, Aly R. ;
Khan, Tufail A. .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2020, 177 :13-23
[6]   Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations [J].
Ahmad, Hijaz ;
Seadawy, Aly R. ;
Khan, Tufail A. ;
Thounthong, Phatiphat .
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2020, 14 (01) :346-358
[7]   Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations [J].
Ahmad, Hijaz ;
Khan, Tufail A. .
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2019, 38 (3-4) :1113-1124
[8]  
[Anonymous], 2010, NONLINEAR SCI LETT A
[9]   Hermite Interpolant Multiscaling Functions for Numerical Solution of the Convection Diffusion Equations [J].
Ashpazzadeh, E. ;
Lakestani, M. .
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2018, 36 (02) :83-97
[10]  
Ates I, 2009, INT J NONLIN SCI NUM, V10, P877