\(A\)-stable parallel block methods for ordinary and integro-differential equations
For the numerical integration of stiff equations \(y'=f(y)\) the authors propose the use of block methods \(Y_{n+1}=AY_ n+hBf(Y_ n)+hDf(Y_{n+1})\) where \(A\), \(B\) and \(D\) are \(k\times k\) matrices. If \(D\) is diagonal and if \(k\) processors are available, then these methods require an amount of work which is similar to what a linear multistep method requires when implemented on a uni-processor machine. However, better stability properties can be achieved. New \(A\)-stable methods of orders 3 and 4 and \(A(\alpha)\)-stable methods \((\alpha > 89.9^ 0)\) of order 5 are presented. The use of these block methods for Volterra integro-differential equations is discussed and some numerical experiments are reported.
Volterra integro- differential equations
scientific article; zbMATH DE number 54680
scientific article