Solution of Linear Systems of Ordinary Differential Equations on an INTEL Hypercube
Copyright policy )Solution of Linear Systems of Ordinary Differential Equations on an INTEL Hypercube
A parallel scheme for the solution of linear systems of ordinary initial value problems (1) \(y'=Ay+f(x)\), \(y(a)=y_ 0\), is developed and tested where \(y\) and \(f\) are \(n\)-dimensional vectors and \(A\) is an \(n\times n\) matrix. The solution is considered on an iPSC/2 INTEL hypercube which is a multiple instruction-multiple data machine, consisting of several processors in hypercube connection. As a result of using the box scheme to discretize (1) one obtains, in parallel, fundamental solutions on subintervals. The resulting systems of equations is solved by a modified version of the recursive doubling technique. The efficiency of three implementations of this algorithm is described in detail. It is shown that this algorithm is easy to program and very flexible, and that machine-dependent optimization is readily achievable. It can be modified slightly to solve boundary value problems.
Linear ordinary differential equations and systems, recursive doubling technique, linear systems, box scheme, multiple instruction-multiple data machine, Parallel numerical computation, parallel processing hypercube, Numerical methods for initial value problems involving ordinary differential equations, fundamental solutions
Linear ordinary differential equations and systems, recursive doubling technique, linear systems, box scheme, multiple instruction-multiple data machine, Parallel numerical computation, parallel processing hypercube, Numerical methods for initial value problems involving ordinary differential equations, fundamental solutions
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