Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations

DOI10.1007/s40314-021-01729-7zbMath1499.65575OpenAlexW4206726559WikidataQ114219309 ScholiaQ114219309MaRDI QIDQ2114998

Anurag Kaur, Higinio Ramos, Vinay Kanwar

Publication date: 15 March 2022

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-021-01729-7

zbMATH Keywords

numerical solutionhybrid block methodnon-linear PDEmodified cubic B-splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Systems of nonlinear first-order PDEs (35F50)

Related Items (5)

A coupled scheme based on uniform algebraic trigonometric tension B-Spline and a hybrid block method for Camassa-Holm and Degasperis-Procesi equations ⋮ Collocation-based numerical simulation of fractional order Allen-Cahn equation ⋮ Numerical solution of time dependent nonlinear partial differential equations using a novel block method coupled with compact finite difference schemes ⋮ An efficient algorithm combining an optimized hybrid block method and the differential quadrature method for solving Hunter-Saxton equation ⋮ An efficient optimized adaptive step-size hybrid block method for integrating \(w^{\prime \prime} = F (t, w, w^\prime)\) directly

Cites Work

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• A hybrid numerical scheme for the numerical solution of the Burgers' equation
• Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method
• A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation
• An accurate approximation algorithm for Burgers' equation in the presence of small viscosity
• Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method
• A numerical method based on Crank-Nicolson scheme for Burgers' equation
• A Jacobi-Gauss-Lobatto collocation method for solving generalized Fitzhugh-Nagumo equation with time-dependent coefficients
• A tenth order \(\mathcal{A} \)-stable two-step hybrid block method for solving initial value problems of ODEs
• Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method
• An analytic study of Fisher's equation by using Adomian decomposition method
• Efficient adaptive step-size formulation of an optimized two-step hybrid block method for directly solving general second-order initial-value problems
• An efficient optimized adaptive step-size hybrid block method for integrating differential systems
• A linear finite difference scheme for generalized time fractional Burgers equation
• An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation
• A Crank-Nicolson approximation for the time fractional Burgers equation
• Mixed-mode oscillations based on complex canard explosion in a fractional-order Fitzhugh-Nagumo model
• Convergence and stability in the numerical integration of ordinary differential equations
• An exponentially fitted method for solving Burgers' equation
• Numerical solutions of generalized Burgers–Fisher and generalized Burgers–Huxley equations using collocation of cubicB-splines
• The finite volume method for solving Buckmaster's equation, Fisher's equation and sine Gordon's equation for PDE's
• Generalized Multistep Predictor-Corrector Methods
• A Runge-Kutta for all Seasons

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