Invariant functions for solving multiplicative discrete and continuous ordinary differential equations

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

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...

Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.

Artificial neural networks for solving ordinary and partial differential equations

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neura...

Ordinary differential equations with inverted functions

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forw...