Thomas Algorithm for Tridiagonal Systems

The Thomas algorithm is well known in nnmerical mathematics as an implementation of Gaussian elimination applied specifically to tridiagonal systems. If each equation is of the form 

A three-equation, three-unknown example is as follows  

A VBA program that implements the Crank-Nicholson method for the problem of Equation 8.5 with the initial and boundary conditions of Equation 8.7 is shown below. Equation 8.15 forms the basis for the tridiagonal system to solve at each time step. 

Dim RacIo As Double Dim NumiXS ceps As Long Dim HaxTime As Double Dim Time As Double Dim T01d() As Double Dim TNewO As Double 

DeltaT = ActiveSheet.Cellsf2 3).Value DeltaX = ActiveSheet CelIs (3, 3). Value Ratio DeltaX 2 / DeltaT 

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