A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations

DOI10.1186/s13662-017-1147-9zbMath1422.65174OpenAlexW2597799595WikidataQ59603894 ScholiaQ59603894MaRDI QIDQ1628654

Ranjan Kumar Mohanty, Gunjan Khurana

Publication date: 4 December 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1147-9

zbMATH Keywords

unconditionally stablemaximum absolute errorstelegraphic equationquasi-linear hyperbolic equationshalf-step grid pointsspline in compression approximations

Mathematics Subject Classification ID

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)

Related Items (4)

Multiple sign-changing solutions for nonlinear fractional Kirchhoff equations ⋮ On the numerical solution of some differential equations with nonlocal integral boundary conditions via Haar wavelet ⋮ A new spline-in-tension method of \(\mathrm{O}(k^{2}+h^{4})\) based on off-step grid points for the solution of 1D quasi-linear hyperbolic partial differential equations in vector form ⋮ Least energy sign-changing solutions for the fractional Schrödinger-Poisson systems in \(\mathbb{R}^3\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• High accuracy non-polynomial spline in compression method for one-space dimensional quasi-linear hyperbolic equations with significant first order space derivative term
• A new fast algorithm based on half-step discretization for one space dimensional quasilinear hyperbolic equations
• High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems
• High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations
• A new compact high order off-step discretization for the system of 2D quasi-linear elliptic partial differential equations
• A new off-step high order approximation for the solution of three-space dimensional nonlinear wave equations
• Spline function approximation for differential equations
• Cubic spline solution of two-point boundary value problems with significant first derivatives
• Difference schemes based on splines in compression for the solution of conservation laws
• Parametric cubic spline approach to the solution of a system of second-order boundary-value problems
• An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation
• A new variable mesh method based on non-polynomial spline in compression approximations for 1D quasilinear hyperbolic equations
• A new high order space derivative discretization for 3D quasi-linear hyperbolic partial differential equations
• A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations
• A new high order compact off-step discretization for the system of 3D quasi-linear elliptic partial differential equations
• A cubic-spline method for solving the wave equation of nonlinear optics
• Numerical solution of singularly perturbed two-point boundary value problems by spline in tension
• Cubic spline for solving singular two-point boundary value problems
• On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients
• A new high accuracy two-level implicit off-step discretization for the system of three space dimensional quasi-linear parabolic partial differential equations
• A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations
• New nonpolynomial spline in compression method of \(O(k^2+k^4)\) for the solution of 1D wave equation in polar coordinates
• A family of nonuniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives
• Spline methods for the solutions of hyperbolic equations
• Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms
• A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications
• Nonpolynomial spline approach to the solution of a system of second-order boundary-value problems
• Parameters spline methods for the solution of hyperbolic equations
• A class of variable mesh spline in compression methods for singularly perturbed two point singular boundary value problems
• Numerical solution of singularly perturbed two point boundary value problems by spline in compression
• High-accuracy cubic spline alternating group explicit methods for 1D quasi-linear parabolic equations†
• An analysis for a high-order difference scheme for numerical solution toutt =A(x, t)uxx +F(x, t, u, ut,ux)
• Non-polynomial cubic spline methods for the solution of parabolic equations
• A New Fast Numerical Method Based on Off-Step Discretization for Two-Dimensional Quasilinear Hyperbolic Partial Differential Equations
• Convergent spline in tension methods for singularly perturbed two-point singular boundary value problems
• A Fully Implicit Finite Difference Approximation to the One-dimensional Wave Equation using a Cubic Spline Technique
• Spline in compression method for the numerical solution of singularly perturbed two-point singular boundary-value problems
• Piecewise Cubic Interpolation and Two-Point Boundary Problems
• The use of cubic splines in the solution of two-point boundary value problems
• A Cubic Spline Technique for the One Dimensional Heat Conduction Equation
• New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations

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