TY - JOUR

T1 - Numerical solution of non-linear algebraic equations with discontinuities

AU - Shacham, Mordechai

AU - Brauner, Neima

PY - 2002/10/15

Y1 - 2002/10/15

N2 - The solution of systems of non-linear algebraic equations with discontinuities in the solution search domain is considered. It is demonstrated that such problems are often very difficult to solve, even with the state of the art numerical solvers, and even when initial guesses close to the solutions are used. The application of constrained solution methods that do not require evaluation of function and derivative values outside of a predefined (feasible) subspace of the variables for solving such systems is considered. An algorithm is presented for identifying and handling of sub-expressions that introduce discontinuities. These are either removed by algebraic manipulations, or defined as boundaries of a feasible subspace. Using the proposed approach, it is demonstrated that a feasible solution for originally unsolvable problems can be found.

AB - The solution of systems of non-linear algebraic equations with discontinuities in the solution search domain is considered. It is demonstrated that such problems are often very difficult to solve, even with the state of the art numerical solvers, and even when initial guesses close to the solutions are used. The application of constrained solution methods that do not require evaluation of function and derivative values outside of a predefined (feasible) subspace of the variables for solving such systems is considered. An algorithm is presented for identifying and handling of sub-expressions that introduce discontinuities. These are either removed by algebraic manipulations, or defined as boundaries of a feasible subspace. Using the proposed approach, it is demonstrated that a feasible solution for originally unsolvable problems can be found.

KW - Constrained non-linear equations

KW - Function discontinuity

KW - Root finding

UR - http://www.scopus.com/inward/record.url?scp=0037107350&partnerID=8YFLogxK

U2 - 10.1016/S0098-1354(02)00122-9

DO - 10.1016/S0098-1354(02)00122-9

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AN - SCOPUS:0037107350

SN - 0098-1354

VL - 26

SP - 1449

EP - 1457

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

IS - 10

ER -