A sixth order backward differentiation formula (BDF) need six (five plus initial value) previous solutions to get started. How I can get these previous solutions? I need a method accurate to sixth order capable of handling stiff problems.
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2 Answers
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The standard approach is to use a self-starting time-marching algorithm with sufficiently small timestep (such that the order of accuracy is not spoiled) and compute the 5 non-initial value previous solutions. These are then used to "start" the BDF formula.
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Just to add a bit to @Jesse Chan's answer: you can preserve 6th-order convergence if you use a 5th-order starting method; in general, the starting method can be one order lower than the multistep method without decreasing the global convergence rate.
The most common starting methods are, of course, Runge-Kutta methods.
answered Apr 16, 2015 at 11:52