The Add_to_Matrix_Equation_Monomial procedure adds the linearized version of the a monomial or the time derivative of a monomial to the specified matrix equation. It currently assumes that there is a one-to-one correspondence between the Monomial locus (e.g. Cells) and the equation and variable numbering, and furthermore assumes that the locus is Cells.

The linearization for a non-time-derivative monomial is as follows:

 42#2C43#3 dV 44#4 CV45#546#6 + E47#748#849#9 - 50#1051#1152#12 (14.1) = CVE47#749#9 + CV53#131 - E54#1446#6 (14.2)

The linearization for a time-derivative monomial is as follows:

 42#2C55#1556#1643#357#17 dV 44#4 58#1859#1946#6 + E47#748#849#9 - 50#1051#11 - 60#2061#21 (14.3) = 62#2247#749#9 + 58#1863#2353#131 - E54#1446#6 - 64#2465#25 (14.4)

where 66#26 is the kth iterate, 67#27 is the past time step value, and 68#28 approaches 69#29 with successive iterations.

Calling syntax:

Input variables:

 Monomial The Monomial Term to be added. ELLM The ELL Matrix to be incremented. RHS_MV The right-hand side Mathematic Vector to be incremented.

Output variables:

 ELLM The ELL Matrix that has been incremented. RHS_MV The right-hand side Mathematic Vector that has been incremented.

Internal variables:

 Matrix_Columns Columns for the added matrix values. Matrix_Rows Rows for the added matrix values. Matrix_Values Calculated values to be added to the matrix or vector.