Related papers: Numerical Solution of Nonclassical Boundary Value …

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…

We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…

For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms…

Using Leray-Schauder degree or degree for $\alpha$-condensing maps we obtain the existence of at least one solution for the boundary value problem of the type \[ \left\{\begin{array}{lll} (\varphi(u' ))' = f(t,u,u') & & \\ u(T)=0=u'(0), & &…

In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…

This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…

In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…

Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…

In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…

We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…

We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…

Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval $[0,1]$ endowed with a linear discontinuous production term, formulated in the space $\mathcal{M}([0,1])$ of…

In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian…

Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…

This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical…