Bidzina Midodashvili

FINITE DIFFERENCE SOLUTION OF A NONLINEAR KLEIN-GORDON EQUATION WITH AN EXTERNAL SOURCE

In this paper, we consider the Darboux problem for a (1+1)-dimensional cubic nonlinear Klein-Gordon equation with an external source. Stable finite difference scheme is constructed on a four-point stencil, which does not require additional iterations for passing from one level to another. It is proved, that the finite difference scheme converges with the rate O(h 2 ), when the exact solution belongs to the Sobolev space W 2 2 .

Method of corrections by higher order differences for elliptic equations with variable coefficients

Abstract We consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate O(|h| m )

Associated immediate probability intuitionistic fuzzy aggregations in MCDM

{O(|h|^m)}

On the improvement of convergence rate of difference schemes with high order differences for a convection-diffusion equation

in the discrete L2-norm, when the solution of the original problem belongs to the Sobolev space with exponent m∈[2,4]

On the solvability of one boundary value problem for some semilinear wave equations with source terms

{m\in [2,4]}

Method of Refinement by Higher Order Differences for 3D Poisson Equation with Nonlocal Boundary Conditions

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One nonlocal problem in time for a semilinear multidimensional wave equation

Abstract In this article, the Associated Immediate Probability Intuitionistic Fuzzy Order Weighted Averaging (As-IP-IFOWA) and the Associated Immediate Probability Intuitionistic Fuzzy Order Weighted Geometric (As-IP-IFOWG) operators are constructed. Associated probability distributions in the role of uncertainty measure are used. Arguments of the new aggregation operators are presented in the intuitionistic fuzzy values. Some properties of the constructed operators are presented. The conjugate intuitionistic fuzzy operator is defined. The conjugate connections between the constructed operators are shown. Several variants of the new operators for the decision making problem regarding assessment of the software development risks are used.

Method of corrections by higher order differences for one nonlocal boundary-value problem

We consider a Dirichlet boundary-value problem for the 3D convection-diffusion equations with variable coefficients at convection terms. For solution of this problem in the unit cube we offer two-stage finite difference method which uses on each stage 7-point stencil for values of the sought function. We prove that the method converges in the discrete L2-norm with the rate O(hm) when the solution of original problem belongs to the Sobolev space W2m, m∈(2,4].