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Numerical Methods of Boundary Layer Type for Stiff Systems of Differential Equations

IP.com Disclosure Number: IPCOM000080138D
Original Publication Date: 1973-Mar-01
Included in the Prior Art Database: 2005-Feb-27
Document File: 2 page(s) / 32K

Publishing Venue

IBM

Related People

Miranker, WL: AUTHOR

Abstract

Consider the initial value problem z = k(t,z), z(0) = Zeta which may be stiff. Here z, k and Zeta are N vectors, t is a scalar and the dot denotes d over dt. Solve the problem numerically along a given mesh with increment h, proceeding in a classical manner as if the system were not stiff. Call the approximation to z(h) so obtained,

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Numerical Methods of Boundary Layer Type for Stiff Systems of Differential Equations

Consider the initial value problem

z = k(t,z), z(0) = Zeta which may be stiff. Here z, k and Zeta are N vectors, t is a scalar and the dot denotes d over dt. Solve the problem numerically along a given mesh with increment h, proceeding in a classical manner as if the system were not stiff. Call the approximation to z(h) so obtained,

Now compare z (h) and Zeta component-wise; i.e., test the following inequality

(Image Omitted)

This methos along with several variationa are described in detail in IBM Research Report RC3881, "Numerical Methods of Boundary Layer Type for Stiff Systems of Differential Equations" by the author.

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