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Published byAngela Hodge Modified over 6 years ago
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Numerical solution of first-order ordinary differential equations
1. First order Runge-Kutta method (Euler’s method) Let’s start with the Taylor series of y(t) expanded at t=t0 We now restrict our solution to a short time step h.
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2. Second order Runge-Kutta method
Approximate derivative at t=t0 Intermediate estimate of y at t = t0+h/2 Estimate of derivative at t = t0+h/2 Estimate of y at t = t0+h
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3. Fourth order Runge-Kutta method
Approximate derivative at t=t0, Intermediate estimate of y at t = t0+h/2 using k1, Estimate of derivative at t = t0+h/2, Intermediate estimate of y at t = t0+h/2 using k2, Estimate of derivative at t = t0+h/2, Intermediate Estimate of y at t = t0+h using k3, Estimate of derivative at t = t0+h,
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4. Real application, vortex Rossby waves
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