Solving Ordinary Differential Equations with Discontinuities

Circulant Preconditioners for Solving Ordinary Differential Equations

In this paper, we consider the solution of ordinary diierential equations using boundary value methods. These methods require the solutions of one or more unsymmetric, large and sparse linear systems. Krylov subspace methods with the Strang block-circulant preconditioners are proposed for solving these linear systems. We prove that our preconditioners are invertible and all the eigenvalues of t...

Odeint - Solving ordinary differential equations in C++

Ordinary differential equations (ODEs) play a crucial role in many scientific disciplines. For example the Newtonian and Hamiltonian mechanics are completely formulated in terms of ODEs. Other important applications can be found in biology (population dynamics or neuroscience), statistical physics and molecular dynamics or in nonlinear sciences [1]. Furthermore, ODEs are used in numerical simul...

Solving Ordinary Differential Equations with Range Conditions. Applications

This paper introduces the problem of solving ordinary differential equations with extra linear conditions written in terms of ranges, and deals with the corresponding existence and uniqueness problems. Some methods for analyzing the existence of solutions and obtaining the set of all solutions, based on the theory of cones and polyhedra, are given. These solutions are found by first converting ...

Ordinary Differential Equations with Fractalnoisef

The diierential equation dx(t) = a(x(t); t) dZ (t) + b(x(t); t) dt for fractal-type functions Z (t) is determined via fractional calculus. Under appropriate conditions we prove existence and uniqueness of a local solution by means of its representation x(t) = h(y(t) +Z(t); t) for certain C 1-functions h and y. The method is also applied to It^ o stochastic diierential equations and leads to a g...

A quasi-interpolation method for solving stiff ordinary differential equations