Name
Title | ||
|---|---|---|
Alternating Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a Positive-Type Memory Term |
Abstract | ||
|---|---|---|
New numerical techniques are presented for the solution of a class of linear partial integro-differential equations (PIDEs) with a positive-type memory term in the unit square. In these methods, orthogonal spline collocation (OSC) is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) methods based on the backward Euler, the Crank-Nicolson, and the second order BDF methods combined with judiciously chosen quadrature rules are considered. The ADI OSC methods are proved to be of optimal accuracy in time and in the $L^2$ norm in space. Numerical results confirm the predicted convergence rates and also exhibit optimal accuracy in the $L^{\infty}$ and $H^1$norms and superconvergence phenomena. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/050634967 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
positive-type memory term,linear partial integro-differential equation,alternating direction implicit orthogonal,adi osc method,evolution equation,numerical result,optimal accuracy,spline collocation methods,orthogonal spline collocation,convergence rate,order bdf method,quadrature rule,new numerical technique,collocation method,alternating direction implicit method,backward euler method,crank nicolson method,alternating direction implicit | Alternating direction implicit method,Discretization,Mathematical optimization,Mathematical analysis,Superconvergence,Rate of convergence,Numerical analysis,Collocation method,Backward Euler method,Mathematics,Crank–Nicolson method | Journal |
Volume | Issue | ISSN |
46 | 1 | 0036-1429 |
Citations | PageRank | References |
12 | 1.27 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Amiya Kumar Pani | 1 | 30 | 4.02 |
| Graeme Fairweather | 2 | 142 | 33.42 |
| Ryan I. Fernandes | 3 | 34 | 5.16 |