Related papers: Initial value problems for quad equations
Ill posed linear and nonlinear initial value problems may be stabilized, that it converted to to well posed initial value problems, by the addition of purely nonscalar linear dispersive terms. This is a stability analog of the Turing…
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the initial condition corresponds to an impasse point of the…
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…
We compute the quadratic embedding constant for complete bipartite graphs with disjoint edges removed. Moreover, we study the quadratic embedding property for theta graphs, i.e., graphs consisting of three paths with common initial points…
We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for…
Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…
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…
This paper presents an approach to study initial-boundary value (IBV) problems for integrable nonlinear differential-difference equations (DDEs) posed on a graph. As an illustrative example, we consider the Ablowitz-Ladik system posed on a…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schr\"odinger equation (INLS) $$ i u_t +\Delta u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where $\lambda=\pm 1$ and $\alpha$,…
We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
Initial boundary value problem on a half-line for the Modified KdV equation is considered with the boundary conditions equal to zero at the origin and initial condition chosen arbitrary decreasing rapidly enough and this problem is plunged…
For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic…
In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we…