Solution of fractional-order Korteweg-de Vries and Burgers’ equations utilizing local meshless method
Imtiaz Ahmad, Hijaz Ahmad, Hadi Rezazadeh, M. Ali Akbar, Mostafa M. A. Khater, Lanre Akinyemi, Adil Jhangeer
Abstract
This paper deals with the numerical solution utilizing local version of the meshless collocation method for time-fraction Korteweg de Vries, Burgers’ and Korteweg de Vries-Burgers’ equations. This technique generates sparse and well-conditioned coefficient matrices when applied on a set of uniform or scattered nodes. To check the accuracy of the proposed local meshless technique three test problems are solved numerically.
Topics & Concepts
MathematicsCollocation (remote sensing)Collocation methodBurgers' equationRegularized meshless methodSet (abstract data type)Korteweg–de Vries equationApplied mathematicsMathematical analysisOrder (exchange)Nonlinear systemSingular boundary methodPartial differential equationPhysicsComputer scienceFinite element methodDifferential equationQuantum mechanicsBoundary element methodProgramming languageThermodynamicsMachine learningFinanceOrdinary differential equationEconomicsFractional Differential Equations SolutionsNumerical methods in engineeringNonlinear Waves and Solitons