Numerical Methods for Ordinary Differential Equations

  title={Numerical Methods for Ordinary Differential Equations},
  author={J. D. Lambert},
and in each case one should label the axes and curves via xlabel, ylabel and legend. One may now experiment with different time spans, initial conditions, and parameters (just a for now). As a second example we encode the molecular switch in equation 29 on page 290 via function dx = switch29(t, x) dx(1, 1) = x(1) − x(1)2− 2 ∗ x(1) ∗ x(2); dx(2, 1) = x(2) − x(2)2− 2 ∗ x(1) ∗ x(2); To better appreciate what ode23 is up to we now embark on our own approximation scheme. It is really just a step… 
Axisymmetric fully spectral code for hyperbolic equations
Examples of solving ODEs given as a Black-Box on the Infinity Computer
Several new methods for solving (1) developed for the new kind of a computer – the Infinity Computer – that is able to work numerically with finite, infinite and infinitesimal numbers are discussed.
GIP integrators for Matrix Riccati Differential Equations
The shifted ODE method for underdamped Langevin MCMC
This paper considers the underdamped Langevin diffusion (ULD) and proposes a numerical approximation using its associated ordinary differential equation (ODE), and shows that the ODE approximation achieves a 2-Wasserstein error of ε in O under the standard smoothness and strong convexity assumptions on the target distribution.
Sensitivity Approximation by the Peano-Baker Series
A new method for numerically approximating sensitivities in parameter-dependent ordinary differential equations (ODEs) based on the PeanoBaker series from control theory is developed, which proves that, under standard regularity assumptions, the error of the method scales as O(∆tmax), where ∆t max is the largest time step used when numerically solving the ODE.
Spectral Deferred Correction Methods for Ordinary Differential Equations
We introduce a new class of methods for the Cauchy problem for ordinary differential equations (ODEs). We begin by converting the original ODE into the corresponding Picard equation and apply a
Symmetries of Runge-Kutta methods
This work introduces axillary varieties MD and proves that they are projective algebraic varieties and formulates a hypothesis on how this method can be generalized to the case b2 = b3 = 0 where two-dimensional symmetries appear.
An Overview of Numerical and Analytical Methods for solving Ordinary Differential Equations.
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology,
Integrating factor techniques applied to the Schr{ö}dinger-like equations. Comparison with Split-Step methods
The nonlinear Schr¨odinger and the Schr¨odinger–Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to