15 papers · ranked by Valyu relevance
Dianchen Lu, Tingting Chen, Baojian Hong
This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions…
Bogdan Căruntu, Constantin Bota
We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a…
Lahoucine Tadoummant, Hammad Khalil, Rachid Echarggaoui, Sarah Aljohani + 2 more
The aim of this paper is to investigate the solution of fractional-order partial differential equations and their coupled systems. A novel method is proposed, which effectively handles these problems under two-point non-local boundary conditions. The method is based on shifted Legendre polynomials, and some new…
Litao Gai, Sudao Bilige, Yingmo Jie
In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on…
Edyta Hetmaniok, Mariusz Pleszczyński, Yasir Khan, Carles Gomez
Recently, a lot of attention has been paid to the field of research connected with the wireless sensor network and industrial internet of things. The solutions found by theorists are next used in practice in such area as smart industries, smart devices, smart home, smart transportation and the like. Therefore, there is…
Srinivasarao Thota, Vivek Kumar Srivastav
Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the…
Ahmed Salem Heilat, Nur Nadiah Abd Hamid, Ahmad Izani Md. Ismail
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, $\lambda _{1}$ and $\lambda _{2}$, play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error…
U. Filobello-Nino, H. Vazquez-Leal, M. M. Rashidi, H. M. Sedighi + 10 more
'A. Perez-Sesma' 'M. Sandoval-Hernandez' 'A. Sarmiento-Reyes' 'A. D. Contreras-Hernandez' 'D. Pereyra-Diaz' 'C. Hoyos-Reyes' 'V. M. Jimenez-Fernandez' 'J. Huerta-Chua' 'F. Castro-Gonzalez' 'J. R. Laguna-Camacho'] This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its…
Mehmet Pakdemirli
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution…
Jinxing Liu, Muhammad Nadeem, M. S. Osman, Yahya Alsayaad
Many scientific phenomena are linked to wave problems. This paper presents an effective and suitable technique for generating approximation solutions to multi-dimensional problems associated with wave propagation. We adopt a new iterative strategy to reduce the numerical work with minimum time efficiency compared to…
Zhimin Hong, Zaizai Yan, Jiao Yan, Guido Germano
In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this…
Waseem Waseem, Muhammad Sulaiman, Poom Kumam, Muhammad Shoaib + 3 more
'Muhammad Asif Zahoor Raja' 'Saeed Islam' 'Hector Vazquez-Leal'] In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown…
Saima Bibi, Syeda Tehmina Ejaz
In numerical methods, fine mesh sizes are often necessary to obtain highly accurate solutions of the differential equations and this increases the memory consumption and decreases the efficiency of the calculation. This paper presents a subdivision collocation algorithm of time-fractional advection diffusion equation…
Tahir Shahzad, Muhammad Ozair Ahmed, Muhammad Zafarullah Baber, Nauman Ahmed + 2 more
'Nauman Ahmed' 'Ali Akgül' 'Sayed M. El Din'] In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel…
Olawanle P. Layeni, Adegbola P. Akinola, Jesse V. Johnson
Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some…