Numerical Methods Library for OCTAVE
Numerical Methods Library for OCTAVE
Numerical Methods Library for OCTAVE
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3.8.2 Implicit Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.8.3 Modified Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.8.4 Fourth-order Rounge-Kutta . . . . . . . . . . . . . . . . . . . . . . . . 213.8.5 Fourth-order predictor . . . . . . . . . . . . . . . . . . . . . . . . . . 213.9 Boundary value problems <strong>for</strong> Ordinary differential Equations . . . . . . . . . . 223.9.1 Shooting method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.9.2 Finite difference method . . . . . . . . . . . . . . . . . . . . . . . . . 243.9.3 Colocation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.10 Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.10.1 Method of lines (<strong>for</strong> Heat equation) . . . . . . . . . . . . . . . . . . . 253.10.2 2-D solver <strong>for</strong> Advection equation . . . . . . . . . . . . . . . . . . . . 263.10.3 2-D solver <strong>for</strong> Heat equation . . . . . . . . . . . . . . . . . . . . . . . 273.10.4 2-D solver <strong>for</strong> Wave equation . . . . . . . . . . . . . . . . . . . . . . 283.10.5 2-D solver <strong>for</strong> the Poisson Equation . . . . . . . . . . . . . . . . . . . 292
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