Related papers: Shooting-Projection Method for Two-Point Boundary …
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…
Nonlinear Schr\"odinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of…
We revisit the problem of solving the one-dimensional wave equation on a domain with moving boundary. In J. Math. Phys. 11, 2679 (1970), Moore introduced an interesting method to do so. As only in rare cases, a closed analytical solution is…
- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
Intuitively, the appearance of true object boundaries varies from image to image. Hence the usual monolithic approach of training a single boundary predictor and applying it to all images regardless of their content is bound to be…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to…
In this paper, we study a spline collocation method for a numerical solution to the optimal transport problem We mainly solve the \MAE with the second boundary condition numerically by proposing a center matching algorithm. We prove a…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…