Extension of Newman’s Numerical Technique To Pentadiagonal Systems Of Equations

Zee, John Van; Kleine, Greg; White, Ralph E.; Newman, John

doi:10.1007/978-1-4613-2795-0_19

Cited by 16 publications

(26 citation statements)

References 5 publications

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“…boundary condition, y = 1 at z = 1 [4] solver indicated that the numerical system was singular (i.e., a zero determinant was indicated). The results are presented in Table II.…”

Section: Resultsmentioning

confidence: 99%

A Comparison of Newman's Numerical Technique and deBoor's Algorithm

Curtis

Evans

White

1989

J. Electrochem. Soc.

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“…boundary condition, y = 1 at z = 1 [4] solver indicated that the numerical system was singular (i.e., a zero determinant was indicated). The results are presented in Table II.…”

Section: Resultsmentioning

confidence: 99%

A Comparison of Newman's Numerical Technique and deBoor's Algorithm

Curtis

Evans

White

1989

J. Electrochem. Soc.

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“…Different discretisations can be used depending on the situation and the accuracy required by the process, i.e. high order discretisations have been used successfully in electrochemical systems (Van Zee, Kleine & White, 1984;Fan & White, 1991). As shown in Fig.…”

Section: Fdmmentioning

confidence: 99%

Comparison of finite difference and control volume methods for solving differential equations

Botte

Ritter

White

2000

Computers & Chemical Engineering

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“…This is a result of using threepoint forward and backward finite difference formulas at the interface boundary to maintain accuracy to O(h2). The pentadiagonal BAND(J) subroutine (8) has been used (9, 1) to solve Eq. [7], but this is costly in terms of computation time because of the unnecessary computations due to the null matrices off the tridiagonal, especially when a large number of nodal points are used.…”

Section: Multiple Regionsmentioning

confidence: 99%

Modification of Newman's BAND(J) Subroutine to Multi‐Region Systems Containing Interior Boundaries: MBAND

Fan

White

1991

J. Electrochem. Soc.

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Newman's BAND(J) subroutine, which has been used widely to solve models of various electrochemical systems, is extended to solve a system of coupled, ordinary differential equations with interior boundary conditions. A set of coupled, linear ordinary differential equations is used to demonstrate the solution procedure. The results show that the extended technique has the same accuracy as that of using pentadiagonal BAND(J), but the execution speed is about five times faster than that of pentadiagonal BAND(J). Using sparse matrix solver Y12MAF to solve the same set of equations takes even longer time than pentadiagonal BAND(J).Electrochemical systems such as batteries and fuel cells consist of multiple regions as demonstrated through several references (i-4). The phenomena that occur in these regions can be modeled mathematically. This procedure yields a coupled set of equations with interior boundary conditions. Newman's BAND(J) subroutine (5, 6) has been used widely to solve systems of coupled, nonlinear ordinary differential equation. This is done by first transforming these sets of differential equations into sets of nonlinear algebraic equations by using finite difference approximations. These sets of nonlinear algebraic equations are then solved by using the Newton-Raphson procedure with BAND(J). This procedure yields sets of linear of algebraic equations of the form JC = G or B(2)X(1) 1 D(2)Y(nj,) A(njl ) B(njl) D(njl) X(njl) Y(nj) A(nj) B(nj)

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Extension of Newman’s Numerical Technique To Pentadiagonal Systems Of Equations

Cited by 16 publications

References 5 publications

A Comparison of Newman's Numerical Technique and deBoor's Algorithm

A Comparison of Newman's Numerical Technique and deBoor's Algorithm

Comparison of finite difference and control volume methods for solving differential equations

Modification of Newman's BAND(J) Subroutine to Multi‐Region Systems Containing Interior Boundaries: MBAND

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