scholarly journals On approximation by splines of solution of boundary problem

1987 ◽  
pp. 30
Author(s):  
S.G. Dronov
Keyword(s):  
Approximate Solution ◽  
Boundary Problem ◽  
Fourth Order ◽  
Solution Method ◽  
Cubic Spline ◽  
Order Of Accuracy ◽  
Approximate Solution Method

For the boundary problem$$y'' + p(x) y' + q(x) y = r(x), \; y(a) = Y_a, \; y(b) = Y_b$$we give the approximate solution method of fourth order of accuracy in the form of cubic spline. For truncated problem ($p(x) \equiv 0$) we establish the prior estimates of error.

scholarly journals On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem

2021 ◽  
Vol 102 (2) ◽  
pp. 45-53
Author(s):  
C. Ashyralyyev ◽  
◽  
G. Akyuz ◽  
◽  
Keyword(s):  
Approximate Solution ◽  
Difference Scheme ◽  
Fourth Order ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Uniqueness Of The Solution ◽  
Accuracy Difference ◽  
The Difference ◽  
Overdetermined Boundary Value Problem ◽  
Coercive Stability

In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi-point overdetermined boundary value problem for multidimensional elliptic partial differential equations.

The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation

2008 ◽  
Vol 15 (1) ◽  
pp. 165-175
Author(s):  
Jemal Rogava ◽  
Mikheil Tsiklauri
Keyword(s):  
Approximate Solution ◽  
Hyperbolic Equation ◽  
Fourth Order ◽  
Operator Function ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Cosine Operator Function ◽  
Decomposition Scheme ◽  
Cosine Operator ◽  
Abstract Hyperbolic Equation

Abstract Using the rational splitting of a cosine operator-function, the fourth order accuracy decomposition scheme is constructed for hyperbolic equation when the principal operator is self-adjoint positively defined and is represented as a sum of two summands. Stability of the constructed scheme is shown and the error of an approximate solution is estimated.

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