An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations

In this study Kuramoto--Sivashinsky(KS) equation has been solved using the collocation method, based on the exponential cubic B-spline approximation together with the Crank Nicolson. The results of the proposed method are compared with both numerical and analytical results by studyinh two text probles.

/pdf/the-exponential-cubic-b-spline-collocation-method-for-the-hi28jqmtbz.pdf

The Exponential Cubic B-Spline Collocation Method for the Kuramoto-Sivashinsky Equation

The main purpose of this work is to obtain the numerical solutions for the Kawahara equation via the Crank–Nicolson–Differential Quadrature Method based on modified cubic B-splines (MCBC-DQM). First, the Kawahara equation has been discretized using Crank–Nicolson scheme. Then, Rubin and Graves linearization technique has been utilized and differential quadrature method has been applied to obtain algebraic equation system. Four different test problems, namely single solitary wave, interaction of two solitary waves, interaction of three solitary waves, and wave generation, have been solved. Next, to be able to test the efficiency and accuracy of the newly applied method, the error norms $$ L _{2}$$
 and $$ L _{\infty }$$
 as well as the three lowest invariants $$ I _{1}$$
 , $$ I _{2}$$
 , and $$ I _{3}$$
 have been computed. Besides those, the relative changes of invariants have been reported. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. The comparison of present results with earlier works showed that the newly method may be provide significant benefit in case of numerical solutions of the other nonlinear differential equations.

An Efficient Approximation to Numerical Solutions for the Kawahara Equation Via Modified Cubic B-Spline Differential Quadrature Method

Two novel analytical solutions to the damped Gardner Kawahara equation and its related equations are reported. Using a suitable ansatz and with the help of the exact solutions of the undamped Gardner Kawahara equation, two general high-accurate approximate analytical solutions are derived. Moreover, the Crank–Nicolson implicit finite difference method is introduced for analyzing the evolution equation numerically. The comparison between the obtained solutions is examined. All the obtained solutions are able to investigate many types of the dissipative traveling wave solutions such as the dissipative solitary and cnoidal waves. Also, the obtained solutions help many researchers understand the mechanisms underlying a variety of nonlinear phenomena that can propagate in optical fiber, physics of plasmas, fluid mechanics, water tank, oceans, and seas. The obtained solutions could be applied for investigating the characteristics of the dissipative higher-order solitary and cnoidal waves in electronegative plasmas. Numerical results depending on the physical plasma parameters are presented.

On the dissipative extended Kawahara solitons and cnoidal waves in a collisional plasma: Novel analytical and numerical solutions

In this article, we apply the method of lines (MOL) for solving the heat equation. The use of MOL yields a system of first–order differential equations with initial value. The solution of this system could be obtained in the form of exponential matrix function. Two approaches could be applied on this problem. The first approach is approximation of the exponential matrix by Taylor expansion, Pade and limit approximations. Using this approach leads to create various explicit and implicit finite difference methods with different stability region and order of accuracy up to six for space and superlinear convergence for time variables. Also, the second approach is a direct method which computes the exponential matrix by applying its eigenvalues and eigenvectors analytically. The direct approach has been applied on one, two and three-dimensional heat equations with Dirichlet, Neumann, Robin and periodic boundary conditions.

Application of finite difference method of lines on the heat equation

Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation

In this work, an algorithm based on method of lines coupled with radial basis functions namely meshless method of lines (MMOL) is presented for the numerical solution of Kawahara, modified Kawahara and KdV Kawahara equations. The motion of a single solitary wave, interaction of two and three solitons and the phenomena of wave generation is discussed. The results are compared with the exact solution and with the results in the relevant literature to show the efficiency of the method.

/pdf/meshless-method-of-lines-for-numerical-solution-of-kawahara-jm6mw1gepv.pdf

Meshless Method of Lines for Numerical Solution of Kawahara Type Equations

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Nagina Bibi

Author Tools

Chat about Author

Papers

Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation

Meshless Method of Lines for Numerical Solution of Kawahara Type Equations