Solving ordinary differential equations in EXCEL using quadrature and interpolation formulas

A quasi-interpolation method for solving stiff ordinary differential equations

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...

On solving Ordinary Differential Equations using Gaussian Processes

We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the other to gradient matching. All methods have greater accuracy than previously suggested Gaussian Process approaches. We also suggest a general approach that can...

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...

Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

This paper focuses on the derivation of diagonally implicit two-point block backward differentiation formulas DI2BBDF for solving first-order initial value problem IVP with two fixed points. The method approximates the solution at two points simultaneously. The implementation and the stability of the proposed method are also discussed. A performance of the DI2BBDF is compared with the existing ...