Cubic spline method for 1D wave equation in polar coordinates

DOI10.5402/2012/302923zbMath1239.65056OpenAlexW2042030996WikidataQ58690741 ScholiaQ58690741MaRDI QIDQ408481

Vijay Dahiya, Rajive Kumar, Ranjan Kumar Mohanty

Publication date: 10 April 2012

Published in: ISRN Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5402/2012/302923

zbMATH Keywords

stabilitynumerical exampleswave equationsfinite differencenonpolynomial cubic spline

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Wave equation (35L05) 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) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (2)

Applying cubic B-spline quasi-interpolation to solve 1D wave equations in polar coordinates ⋮ Cubic spline iterative method for Poisson's equation in cylindrical polar coordinates

Cites Work

• An unconditionally stable spline difference scheme of \(O(k^2+h^4)\) for solving the second-order 1D linear hyperbolic equation
• Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation
• A new unconditionally stable compact difference scheme of \(O(\tau ^2+h^4)\) for the 1D linear hyperbolic equation
• Cubic spline solution of two-point boundary value problems with significant first derivatives
• 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 cubic-spline method for solving the wave equation of nonlinear optics
• On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients
• 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
• Parameters spline methods for the solution of hyperbolic equations
• High order compact solution of the one-space-dimensional linear hyperbolic equation
• A Fully Implicit Finite Difference Approximation to the One-dimensional Wave Equation using a Cubic Spline Technique
• Spline methods for the solution of hyperbolic equation with variable coefficients
• Piecewise Cubic Interpolation and Two-Point Boundary Problems
• The use of cubic splines in the solution of two-point boundary value problems
• New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations

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