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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 t ime 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) ~ c(1) 7 FG(1) 7 I~ x = [7]

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