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In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve $3 \times 3$ matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schr\"odinger (NLS) equation on the half-line subject to a class of boundary conditions. The method is based on the notions of integrable…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
In this paper, we use the optimization formulation of nonlinear Kalman filtering and smoothing problems to develop second-order variants of iterated Kalman smoother (IKS) methods. We show that Newton's method corresponds to a recursion over…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
In this study, we derive an analytical solution to address the problem of one-dimensional vertical infiltration within bounded profiles. We consider the Richards equation together with various boundary conditions, simulating different…
Solutions to differential equations, which are used to model physical systems, are computed numerically by solving a set of discretized equations. This set of discretized equations is reduced to a large linear system, whose solution is…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual…