Unconditional Convergence in Maximum-Norm of a Second-Order Linearized Scheme for a Time-Fractional Burgers-Type Equation

2018 ◽  
Vol 76 (2) ◽  
pp. 1252-1273 ◽  
Author(s):  
Seakweng Vong ◽  
Pin Lyu
Keyword(s):  
Type Equation ◽  
Second Order ◽  
Maximum Norm ◽  
Unconditional Convergence ◽  
Convergence In Maximum Norm ◽  
Linearized Scheme

scholarly journals Find A General Solution Of An Equation Of The Hyperbolic Type With A Second-Order Singular Coefficient And Solve The Cauchy Problem Posed For This Equation.

2021 ◽  
Vol 25 (1) ◽  
pp. 80
Author(s):  
Karimova Shalola Musayevna ◽  
Melikuzieva Dilshoda Mukhtorjon qizi
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Type Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Singular Coefficient ◽  
The Cauchy Problem

This paper presents a general solution of a hyperbolic type equation with a second-order singular coefficient and a solution to the Cauchy problem posed for this equation.

scholarly journals Iterative method for solving the second boundary value problem (BVP) for Biharmonic type equation

2016 ◽  
Vol 14 (4) ◽  
pp. 66-72
Author(s):  
Đặng Quang Á
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Second Order ◽  
Second Order Equations

Solving BVPs for the fourth order differential equations by the reduction of them to BVPs for the  second order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by  ourselves in recent works, we construct iterative method for the second BVP for  biharmonic type equation. The convergence rate of  the method is established.

21.—Runge's Theorem for Parabolic Equations in Two Space Variables

1975 ◽  
Vol 73 ◽  
pp. 307-315 ◽  
Author(s):  
David Colton
Keyword(s):  
Parabolic Equation ◽  
Strong Solution ◽  
Parabolic Equations ◽  
Entire Solution ◽  
Second Order ◽  
Maximum Norm ◽  
Cylindrical Domain ◽  
Order Parabolic Equation ◽  
Compact Subsets

SynopsisLet u be a real valued strong solution defined in a cylindrical domain of a linear second-order parabolic equation in two space variables with entire coefficients. Then it is shown that on compact subsets of its domain of definition u can be approximated arbitrarily closely in the maximum norm by an entire solution of the parabolic equation.

The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight

2006 ◽  
Vol 13 (3) ◽  
pp. 573-579
Author(s):  
Mikheil Usanetashvili
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
General Type ◽  
Type Equation ◽  
Second Order ◽  
Elliptic Type ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

Abstract The first boundary value problem with weight is investigated for a general-type second order elliptic type equation degenerating on the whole boundary.

On Finite Volume Discretization of the Three-dimensional Biot Poroelasticity System in Multilayer Domains

2006 ◽  
Vol 6 (3) ◽  
pp. 306-325 ◽  
Author(s):  
A. Naumovich
Keyword(s):  
Physical Properties ◽  
Finite Volume ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Second Order ◽  
Maximum Norm ◽  
Order Convergence ◽  
Staggered Grids ◽  
Finite Volume Discretization ◽  
Second Order Convergence

AbstractIn this paper we propose a finite volume discretization for the threedimensional Biot poroelasticity system in multilayer domains. For stability reasons, staggered grids are used. The discretization takes into account discontinuity of the coefficients across the interfaces between layers with different physical properties. Numerical experiments based on the proposed discretization showed second order convergence in the maximum norm for the primary and flux unknowns of the system. An application example is presented as well.

REGULARIZED DIFFERENCE SCHEMES FOR EVOLUTIONARY SECOND ORDER EQUATIONS

1992 ◽  
Vol 02 (03) ◽  
pp. 295-315 ◽  
Author(s):  
ALEKSANDR A. SAMARSKII ◽  
PETER N. VABISHCHEVICH
Keyword(s):  
Initial Conditions ◽  
Type Equation ◽  
Second Order ◽  
Difference Schemes ◽  
Inversion Method ◽  
Extension Problem ◽  
Elliptic Type ◽  
The Stability ◽  
Well Posed ◽  
Second Order Equations

The questions of approximate solution of unstable problems for evolutionary second order equations are discussed in this paper. The classical Cauchy problem for elliptic type equation is a significant example of such problem. Incorrectness of this problem (the Hadamard example) is due to instability of the solution towards small perturbations of the initial conditions. The extension problem of the solutions of well-posed elliptic problems beyond the calculation region boundary is also discussed. The stability of corresponding difference schemes is investigated by basing on general theory of ρ-stability. The principle of the regularization of three-layer difference schemes is developed for the unstable problems. It is shown that the regularized difference schemes correspond to some modification of quasi-inversion method.

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