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

作者：Pani Amiya Kumar; Fairweather Graeme^*; Fernandes Ryan I

来源：IMA Journal of Numerical Analysis, 2010, 30(1): 248-276.

DOI：10.1093/imanum/drp024

• parabolic partial integro-differential equation
• alternating direction implicit method
• orthogonal spline collocation
• theta-method
• backward Euler method
• Crank-Nicolson method
• second-order BDF method
• optimal convergence rates
• superconvergence

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 theta-method, for theta is an element of [1/2, 1], (where theta = 1 yields the backward Euler method and theta = 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.

• 出版日期2010-1