Spline methods for the solution of fourth-order parabolic partial differential equations

DOI10.1016/j.amc.2004.06.095zbMath1082.65564OpenAlexW2024299142MaRDI QIDQ2570698

Yanyan Li

Publication date: 28 October 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2004.06.095

zbMATH Keywords

comparison of methodsnumerical examplesfinite differenceStability analysisClass of methodsFourth-order parabolic equationParametric quintic splineSpline relationsthree level methodVibrating beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for higher-order parabolic equations (35K30)

Related Items (25)

Numerical analysis of fractional-order parabolic equations via Elzaki transform ⋮ Sextic B-spline collocation method for solving Euler-Bernoulli beam models ⋮ Spline methods for the solutions of hyperbolic equations ⋮ B-spline and singular higher-order boundary value problems ⋮ Quintic Spline functions and Fredholm integral equation ⋮ A numerical approach for the analytical solution of the fourth-order parabolic partial differential equations ⋮ An adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models ⋮ Unnamed Item ⋮ Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients ⋮ Unnamed Item ⋮ Two Efficient Methods For Solving Non-linear Fourth-Order PDEs ⋮ A class of two-level implicit unconditionally stable methods for a fourth order parabolic equation ⋮ Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations ⋮ A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method ⋮ Numerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation method ⋮ Unconditionally stable compact theta schemes for solving the linear and semi-linear fourth-order diffusion equations ⋮ B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations ⋮ Local polynomial regression solution for partial differential equations with initial and boundary values ⋮ Sextic spline solution of variable coefficient fourth-order parabolic equations ⋮ Parameters spline methods for the solution of hyperbolic equations ⋮ Unconditionally stable high accuracy compact difference schemes for multi-space dimensional vibration problems with simply supported boundary conditions ⋮ Determination of the time-dependent thermal grooving coefficient ⋮ A Legendre-Laguerre-Galerkin Method for Uniform Euler-Bernoulli Beam Equation ⋮ Numerical Methods Based on Non-Polynomial Sextic Spline for Solution of Variable Coefficient Fourth-Order Wave Equations ⋮ High order spline finite element method for the fourth-order parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Alternating direction and semi-explicit difference methods for parabolic partial differential equations
• Spline function approximation for differential equations
• Noise terms in decomposition solution series
• Analytic treatment for variable coefficient fourth-order parabolic partial differential equations
• A direct approach to the problem of stability in the numerical solution of partial differential equations
• Convergence of Finite Difference Solutions to a Solution of the Equation of the Vibrating Rod
• The Solution of the Diffusion Equation by a High Order Correct Difference Equation
• Zum Differenzenverfahren bei parabolischen Differentialgleichungen
• A note on solving the fourth order parabolic equation by the age method
• Higher order difference formulas for a fourth order parabolic partial differential equation
• On the solution of the fourth order parabolic equation by the decomposition method
• A stable explicit method for the finite-difference solution of a fourth-order parabolic partial differential equation
• Some Stable Difference Approximations to a Fourth-Order Parabolic Partial Differential Equation

This page was built for publication: Spline methods for the solution of fourth-order parabolic partial differential equations