scholarly journals Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator

2021 ◽  
Vol 165 ◽  
pp. 414-430
Author(s):  
Petr N. Vabishchevich
Keyword(s):  
Rational Approximation ◽  
Fractional Powers ◽  
Splitting Schemes ◽  
Stationary Problems

scholarly journals A Splitting Scheme to Solve an Equation for Fractional Powers of Elliptic Operators

2016 ◽  
Vol 16 (1) ◽  
pp. 161-174 ◽  
Author(s):  
Petr N. Vabishchevich
Keyword(s):  
Dirichlet Boundary ◽  
Model Problem ◽  
Fractional Power ◽  
Dirichlet Boundary Conditions ◽  
Splitting Scheme ◽  
Fractional Powers ◽  
Splitting Schemes ◽  
Unconditionally Stable ◽  
Spatial Variables ◽  
Finite Difference Approximations

AbstractAn equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an auxiliary Cauchy problem for a pseudo-parabolic equation. Unconditionally stable vector-additive schemes (splitting schemes) are constructed. Numerical results for a model problem in a rectangle calculated using the splitting with respect to spatial variables are presented.

Rational Approximation of Real Functions

1988 ◽  
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov
Keyword(s):  
Rational Approximation ◽  
Real Functions

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

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