Alternating-direction method for a mildly nonlinear elliptic equation with nonlocal integral conditions

Sapagovas, Mifodijus; Štikonienė, Olga

doi:10.15388/na.16.2.14107

Cited by 18 publications

(16 citation statements)

References 23 publications

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“…Systems 12- (14) and 18, (19), (16), (14) are equivalent. So 12- 14is being reduced to two separate systems of lower order: one system is (18), (19), (14) and the other system is (16). In system (18), (19), (14) only the unknowns z ij , i, j = 1, N -1, in the internal points of the domain D are presented.…”

Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

“…So 12- 14is being reduced to two separate systems of lower order: one system is (18), (19), (14) and the other system is (16). In system (18), (19), (14) only the unknowns z ij , i, j = 1, N -1, in the internal points of the domain D are presented. So the number of equations and unknowns in the system is equal to (N -1) 2 .…”

Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

“…Furthermore, the unknowns z 0j in (16) are expressed by unknowns z ij , i, j = 1, N -1. This allows us to first solve (18), (19), (14) and 16only afterwards. Now we write system (18), (19), (14) in the matrix form:…”

Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

“…Various iterative methods for the systems of linear difference equations, derived from elliptic equations with nonlocal conditions, and proofs of convergence of these methods can be found in [13][14][15]. In the articles [16][17][18][19], the iterative methods are generalized for the systems of nonlinear difference equations with nonlocal conditions. Some other difference methods for elliptic equations with nonlocal conditions were described in [13,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

et al. 2019

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In the paper the convergence of a finite difference scheme for two-dimensional nonlinear elliptic equation in the rectangular domain with the integral boundary condition is considered. The majorant is constructed for the error of the solution of the system of difference equations, and the estimation of this error is obtained. With this aim, the idea of application of the M-matrices for the theoretical investigation of the system of difference equations was developed. Main results for the convergence of the difference schemes are obtained considering the structure of the spectrum and properties of the M-matrices for a wider class of boundary value problems for nonlinear equations with nonlocal conditions. The main advantage of the suggested method is that the error of approximate solution is estimated in the maximum norm.

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Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

Section: The Investigation Of the Difference Problem For The Errormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

et al. 2019

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“…Iterative methods for systems of nonlinear difference equations with nonlocal conditions were considered in [9,31] (also see paper [36] close to the subject area).…”

Section: Introductionmentioning

confidence: 99%

Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition

Sapagovas

Griškonienė

Štikonienė

2017

NAMC

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The iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowledge, the theory of M-matrices has not ever been applied to convergence of iterative methods for system of nonlinear difference equations. The main results for the convergence of the iterative methods are obtained by considering the structure of the spectrum of the twodimensional difference operators with integral condition.

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Stability of the space identification problem for the elliptic‐telegraph differential equation

Ashyralyev

Al-Hammouri²

2020

Math Methods in App Sciences

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The present paper is devoted to study the space identification problem for the elliptic-telegraph differential equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the space identification problem for the elliptic-telegraph differential equation is proved. In applications, theorems on the stability of three source identification problems for one dimensional with nonlocal conditions and multidimensional elliptic-telegraph differential equations are established.

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Alternating-direction method for a mildly nonlinear elliptic equation with nonlocal integral conditions

Cited by 18 publications

References 23 publications

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition

Stability of the space identification problem for the elliptic‐telegraph differential equation

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