Septic Hermite collocation method for the numerical solution of Benjamin–Bona–Mahony–Burgers equation
A. Kumari, V. K. Kukreja
Abstract
In this paper, the nonlinear Benjamin–Bona–Mahony–Burgers (BBMB) equation is solved using the septic Hermite collocation method (SHCM) for the space discretization and Crank–Nicholson scheme for the time discretization. The Von-Neumann stability analysis is used to show the unconditional stability of the proposed method. The error bounds for the septic Hermite interpolation polynomials are estimated using the Peano's theorem. The method is applied to one, two and three interaction solitary wave problems. The L2 and L∞ error norms are calculated to demonstrate the efficiency and the robustness of the proposed technique.
Topics & Concepts
MathematicsDiscretizationHermite polynomialsBurgers' equationMathematical analysisApplied mathematicsCollocation methodPartial differential equationDifferential equationOrdinary differential equationNonlinear Waves and SolitonsFractional Differential Equations SolutionsNumerical methods in engineering