OPDE

Revision for “OPDE” created on April 15, 2015 @ 18:26:09

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OPDE
This is a collection of numerical algorithms to solve ordinary and partial differential equation problems.

<ul>
<li>Ordinary Differential Equation (ODE) solvers for initial value problem (IVP):
<ul>
<li>Euler’s method</li>
<li>Runge Kutta
<ul>
<li>1st order Runge Kutta</li>
<li>2nd order Runge Kutta</li>
<li>3rd order Runge Kutta</li>
<li>4th order Runge Kutta</li>
<li>5th order Runge Kutta</li>
<li>6th order Runge Kutta</li>
<li>7th order Runge Kutta</li>
<li>8th order Runge Kutta</li>
<li>10th order Runge Kutta</li>
</ul>
</li>
<li>Runge-Kutta-Fehlberg (RKF45) (adaptive step-size control)</li>
<li>Adams-Bashforth-Moulton predictor-corrector multi-step method
<ul>
<li>1st order</li>
<li>2nd order</li>
<li>3rd order</li>
<li>4th order</li>
<li>5th order</li>
</ul>
</li>
<li>solvers based on Richardson extrapolation
<ul>
<li>Burlisch-Stoer extrapolation</li>
<li>semi-implicit extrapolation (suitable for stiff systems)</li>
</ul>
</li>
<li>first order system of ODEs</li>
<li>conversion from high order ODE to first order ODE system</li>
</ul>
</li>
</ul>
<ul>
<li>Partial Differential Equation (PDE) solvers
<ul>
<li>finite difference methods:
<ul>
<li>elliptic problem:
<ul>
<li>iterative central difference method (for Poisson’s equation)</li>
</ul>
</li>
<li>1D hyperbolic problem:
<ul>
<li>explicit central difference method (for 1D wave equation)</li>
</ul>
</li>
<li>2D hyperbolic problem:
<ul>
<li>explicit central difference method (for 2D wave equation)</li>
</ul>
</li>
<li>1D parabolic problem:
<ul>
<li>Crank-Nicolson method (for 1D heat or diffusion equation)</li>
</ul>
</li>
<li>2D parabolic problem:
<ul>
<li>alternating direction implicit (ADI) method (for 2D heat or diffusion equation)</li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>



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April 15, 2015 @ 18:26:09 webmaster
April 13, 2015 @ 10:47:45 sanjay
April 13, 2015 @ 08:30:58 sanjay