Quasi Trefftz Spectral Method for Stokes Problem

1997 ◽  
Vol 07 (08) ◽  
pp. 1187-1212 ◽  
Author(s):  
S. A. Lifits ◽  
S. Yu. Reutskiy ◽  
G. Pontrelli ◽  
B. Tirozzi
Keyword(s):  
Free Boundary ◽  
Spectral Method ◽  
Initial Value Problems ◽  
Moving Boundary ◽  
Stokes Problem ◽  
Boundary Value ◽  
Elliptic Operators ◽  
Initial Value ◽  
Primitive Variables

A new numerical Quasi Trefftz Spectral Method (QTSM) which was earlier suggested for solving boundary value and initial value problems with elliptic operators is applied to linear stationary hydrodynamic problems. The primitive variables [Formula: see text] are used. The method has been found to work well for different problems, including free boundary ones. The problem of the Stefan type in the domain with moving boundary is also considered. The possibilities of further developments of QTSM are discussed.

scholarly journals Spectral approximations to the fractional integral and derivative

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Changpin Li ◽  
Fanhai Zeng ◽  
Fawang Liu
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Caputo Derivative ◽  
Initial Value Problems ◽  
Fractional Integral ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
Initial Value ◽  
Numerical Examples ◽  
Spectral Approximations

AbstractIn this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

scholarly journals Multi-Derivative Multistep Method for Initial Value Problems Using Boundary Value Technique

OALib ◽  
2020 ◽  
Vol 07 (03) ◽  
pp. 1-17
Author(s):  
Emmanuel A. Areo ◽  
Oluwatoyin A. Edwin
Keyword(s):  
Initial Value Problems ◽  
Boundary Value ◽  
Multistep Method ◽  
Initial Value

scholarly journals A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
A. Karimi Dizicheh ◽  
F. Ismail ◽  
M. Tavassoli Kajani ◽  
Mohammad Maleki
Keyword(s):  
Differential Equation ◽  
Spectral Method ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Runge Kutta Method ◽  
Collocation Points ◽  
Oscillatory Initial Value Problems ◽  
Exponentially Fitted

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

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