ADI orthogonal spline collocation methods for parabolic partial integro-differential equations

Alternating direction implicit (ADI) orthogonal spline collocation schemes are formulated and analysed for a class of partial integro-differential equations of parabolic type. These techniques are based on the -method, for [1/2, 1], (where = 1 yields the backward Euler method and = 1/2 yields the Crank–Nicolson method) and the second-order backward differentiation formula (BDF) method. For each method, optimal estimates in various norms at each time step are derived and confirmed by results of numerical experiments.

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Original source : http://imajna.oxfordjournals.org/cgi/content/short...