Wavelet based method for solving generalized Burger’s type equations

2019 ◽  
Vol 08 (04) ◽  
pp. 1950020
Author(s):  
Inderdeep Singh
Keyword(s):  
Differential Equations ◽  
Algebraic System ◽  
Numerical Experiments ◽  
Nonlinear Differential Equations ◽  
Linear Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Haar Wavelet ◽  
Nonlinear Ordinary Differential Equation ◽  
System Of Linear Equations

In this work, an efficient numerical method is proposed for solving generalized Burger’s type equations. The generalized Burger’s type equations are first converted into a nonlinear ordinary differential equation by choosing some suitable wave variable transformation. Linearize such nonlinear differential equations by using quasilinearization technique. For solving algebraic system of linear equations Haar wavelet-based collocation method is used. A distinct feature of the proposed method is their simple applicability in a variety of two- and three- dimensional nonlinear partial differential equations. Numerical experiments are performed to illustrate the accuracy and efficiency of the proposed method.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

Haar wavelet operational matrix method for system of fractional nonlinear differential equations

2017 ◽  
Vol 15 (05) ◽  
pp. 1750043 ◽  
Author(s):  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Reliable Method ◽  
Nonlinear Differential Equations ◽  
Operational Matrix ◽  
Implementation Process ◽  
Haar Wavelet ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
Fractional Differential

In this paper, we present a reliable method for solving system of fractional nonlinear differential equations. The proposed technique utilizes the Haar wavelets in conjunction with a quasilinearization technique. The operational matrices are derived and used to reduce each equation in a system of fractional differential equations to a system of algebraic equations. Convergence analysis and implementation process for the proposed technique are presented. Numerical examples are provided to illustrate the applicability and accuracy of the technique.

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

2021 ◽  
Vol 10 (9) ◽  
pp. 3273-3282
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Flow Model ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

scholarly journals Approximate Solutions of Nonlinear Partial Differential Equations by Modifiedq-Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Shaheed N. Huseen ◽  
Said R. Grace
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
Power Series Solution ◽  
Analysis Method ◽  
Exactly Solvable ◽  
Homotopy Analysis

A modifiedq-homotopy analysis method (mq-HAM) was proposed for solvingnth-order nonlinear differential equations. This method improves the convergence of the series solution in thenHAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting thenth-order nonlinear differential equation in the form ofnfirst-order differential equations. The solution of thesendifferential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

scholarly journals New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Faruk Dusunceli
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Ordinary Differential Equation ◽  
Wave Transformation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Parameter Values ◽  
Singular Soliton

The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.

scholarly journals Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Flow ◽  
Finite Radius ◽  
Similarity Transformations ◽  
Moving Cylinder ◽  
Micropolar Nanofluid ◽  
Homotopy Analysis ◽  
Flow Phenomena

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.

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