Collocation methods for parabolic partial differential equations in one space dimension

DOI10.1007/BF01395944zbMath0362.65094MaRDI QIDQ1240038

Seymour V. Parter, John H. Cerutti

Publication date: 1976

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132412

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Initial-boundary value problems for second-order parabolic equations (35K20)

Related Items (18)

A class of conservative orthogonal spline collocation schemes for solving coupled Klein-Gordon-Schrödinger equations ⋮ The solution of nonlinear Schrödinger equations using orthogonal spline collocation ⋮ Collocation Approximation to Eigenvalues of an Ordinary Differential Equation: The Principle of the Thing ⋮ A remark on the eigenvalue distribution of the preconditioning collocation scheme with \(P_ 3\) finite element stiffness matrix ⋮ Continuous time collocation methods for Volterra-Fredholm integral equations ⋮ Collocation in space and time: Experience with the Korteweg-de Vries equation ⋮ A \(C^ 1\) finite element collocation method for the equations of one- dimensional nonlinear thermoviscoelasticity ⋮ Piecewise polynomial approximation of a nonlocal phase transitions model ⋮ Numerical approximation of a convolution model of \(\dot{\theta}\)-neuron networks ⋮ Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator ⋮ Orthogonal Spline Collocation Laplace-Modified and Alternating-Direction Methods for Parabolic Problems on Rectangles ⋮ An alternating direction implicit method for orthogonal spline collocation linear systems ⋮ A single-node characteristic collocation method for unsteady-state convection-diffusion equations in three-dimensional spaces ⋮ Orthogonal spline collocation methods for partial differential equations ⋮ Analysis on eigenvalues for preconditioning cubic spline collocation method of elliptic equations ⋮ Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions ⋮ Preconditioning \(C^ 1\) Lagrange polynomial spline collocation method of elliptic equations by finite element method. ⋮ A collocation finite element method for integration of the boundary layer equations

Cites Work

• Collocation for systems of boundary value problems
• High order projection methods of moment- and collocation-type for nonlinear boundary value problems
• Collocation at Gaussian Points
• A Finite Element Collocation Method for Quasilinear Parabolic Equations
• What is the Laplace Transform?
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