A Spectral Collocation Approach for Time-Fractional Korteweg-de Vries-Burgers Equation via First-Kind Chebyshev Polynomials
Y. H. Youssri, Laila A. Alnaser, Ahmed Gamal Atta
Abstract
The time-fractional Korteweg-de Vries-Burgers (TFKdVB) problem is solved numerically in this study. The approach makes use of the shifted first-kind Chebyshev polynomials (SFKCPs) collocation method. By utilizing Caputo's formulation to approximate the time-fractional derivatives and impose boundary conditions, we arrive at a spectral solution. Numerical examples are presented to illustrate the precision and effectiveness of the suggested approach.
Topics & Concepts
MathematicsChebyshev polynomialsBurgers' equationChebyshev filterChebyshev equationKorteweg–de Vries equationClassical orthogonal polynomialsPure mathematicsCollocation (remote sensing)Orthogonal polynomialsJacobi polynomialsMathematical analysisApplied mathematicsPartial differential equationNonlinear systemQuantum mechanicsRemote sensingGeologyPhysicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsIterative Methods for Nonlinear Equations