The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-Axially Symmetric Potentials (GBASP′s). The GBASP′s are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is stu...

In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, obtain two approximation results, namely, BSDE and numerical approximation. The means that solution finite system differential (BSDEs) converges to M-solution original equation. As consequence approximation, an estimate for L 2 -time regularity M-solutions BSVIEs. pr...

In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence b...

We present several new standard and differential approximation results for P4-partition problem by using the algorithm proposed in Hassin and Rubinstein (Information Processing Letters, 63: 63-67, 1997), for both minimization and maximization versions of the problem. However, the main point of this paper is the robustness of this algorithm, since it provides good solutions, whatever version of ...

The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...

The Regge-Wheeler equation describes axial perturbations of Schwarzschild metric in linear approximation. Teukolsky Master Equation describes perturbations of Kerr metric in the same approximation. We present here unified description of all classes of exact solutions to these equations in terms of the confluent Heun’s functions. Special attention is paid to the polynomial solutions, which yield...

Precise estimates for the validity of the amplitude approximation for the Swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of order O() which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of order O(?2). For the proofs, we use techniques for nonlinear semigroups...

In this paper, the differential transform method and Padé approximation (DTM-Padé) is applied to obtain the approximate analytical solutions of the MHD flow and heat transfer of a nanofluid over a nonlinearly stretching permeable sheet in porous. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations...

In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compa...

A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the complete first-order corrections in the short-wavelength limit to eigenmodes and eigenfrequencies in a Fabry-Perot resonator with perfectly conducting mirrors....