A Convergent Scheme for Solving Initial Value Problems with Polynomial and Exponential Functions
, 2021 This paper presents the development of a convergent numerical scheme for the solution of initial value problems of first order ordinary differential equations.
Qureshi, Sania +2 more
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The Partition of Unity Method for the Elastically Supported Beam
, 1998 The partition of unity method (PUM) is used to solve the Timoshenko beam with elastic support. Some important features of this new method are addressed, but the main concern is to overcome locking and boundary layer.
Ivo Babuska, Zhimin Zhang
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PROPOSITIONS on the ROBUSTNESS of MULTISTEP FORMULAE
, 1994 Classical analysis of linear multistep formulae (LMFs) for initial-value problems in ordinary differential equations (ODEs) has concentrated on problems satisfying uniform Lipschitz or one-sided Lipschitz conditions, and corresponding stability models ...
Christopher T.H. Baker
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Sixth-Order Hybrid Block Method for the Numerical Solution of First Order Initial Value Problems
, 2013 Hybrid block method of order six is proposed in this paper for the numerical solution of first order initial value problems. The method is based on collocation of the differential system and interpolation of the approximate at the grid and off-grid ...
AREO, E. A., ADENIYI, R.B.
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Single Step Smooth Interface for Parabolic Spectral Elements
, 2007 A method is examined to calculate a smooth interface for spectral elements. The idea of the method is to find a polynomial of one less degree that interpolates the interior and one side of a subdomain.
Kelly Black
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Stable Parallel Elimination For Boundary Value Odes
, 1991 . A parallelizable and vectorizable algorithm for solving linear algebraic systems arising from two-point boundary value ODEs is described. The method is equivalent to Gaussian elimination, with row partial pivoting, applied to a certain row- and column-
Stephen Wright
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Multiresolutional Methods for Difference Equations
, 1994 . We develop a stable direct method with linear complexity for solving large banded sparse linear systems which are typical for the finite difference discretization of one-dimensional differential equations.
Wei-Chang Shann, I-Liang Chern
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Exploiting structure in the construction of DIMSIMs
, 1997 . We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations.
H. D. Mittelmann, Z. Jackiewicz
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Decoupled Smooth Interfaces for Spectral-Element Approximations of Parabolic or Elliptic Type
, 2007 A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method.
Kelly Black
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Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. [PDF]
Heliyon, 2023 Berrone S +3 more
europepmc +1 more source