First order partial differential equations (PDE) are often the main tool to model problems in optimal control, differential games, image processing, physics, etc. Dependent upon the particular application, the boundary conditions are specified either at the initial time instant, leading to an initial value problem (IVP), or at the terminal time instant, leading to a terminal value problem (TVP)...

The paper is concerned with the computational complexity of the initial value problem (IVP) for a system of ordinary dynamical equations. Formal problem statement is given, containing a Turing machine with an oracle for getting the initial values as real numbers. It is proven that the computational complexity of the IVP for the three body problem is not bounded by a polynomial. The proof is bas...

We announce publicly available Fortran 90 software for the initial value problem (IVP) in ordinary diierential equations (ODEs). We describe the interfaces and how Fortran 90 language features aaord the opportunity both to address diierent types and structures of variables and to provide functionality not usually directly associated with IVP solvers.

We announce publicly available Fortran software for the initial value problem IVP in ordinary di erential equations ODEs We describe the interfaces and how Fortran language features a ord the opportunity both to address di erent types and structures of variables and to provide functionality not usually directly associated with IVP solvers

In this paper, we consider the problem of recovery a burst-like forcing term in an initial value (IVP) framework dynamical sampling. We introduce idea using two particular classes samplers that allow one to predict solution IVP over time interval without burst. This leads different algorithms stably and accurately approximate even presence measurement acquisition error large background source.

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

We study the initial value problem (IVP) associated to some canonical dispersive equations. Our main concern is to establish the minimal regularity property required in the data which guarantees the local well-posedness of the problem. Measuring this regularity in the classical Sobolev spaces, we show ill-posedness results for Sobolev index above the value suggested by the scaling argument.

subject to the initial condition xðt0Þ 1⁄4 x0; t0 $ 0; x0 [ R; ð2Þ where f : 1⁄20;1Þ £ R ! R is a continuous function and t is from a so-called “time scale” T (which is a nonempty closed subset of R). Equation (1) subject to Eq. (2) is known as an initial value problem (IVP) on time scales. If T 1⁄4 R then x 1⁄4 x 0 and Eqs. (1) and (2) become the following IVP for ordinary differential equatio...

We present a new type of neural network (NN) where the data for the input layer are the value x in R, the vector y in R(m ) associated to an initial value problem (IVP) with y'(x)= f(y(x)) and a steplength h. Then the stages of a Runge-Kutta (RK) method with trainable coefficients are used as hidden layers for the integration of the IVP using f as transfer function. We take as output two estima...

An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic derivation, the Pontryagin’s Minimum Principle (PMP) optimality conditions are used. Techniques including limited integrator and corner points are introduced to capt...