Nomenclature

The following will be used throughout this course

eps_step
If and represent two successive approximations of a value , one condition for halting is that .
eps_abs
If and represent two successive approximations of a value , one condition for halting is that .
f
A function used in an algorithm, either for root finding () or an initial value-problem ().
g
A forcing function of a 2nd-order ordinary differnetial equation.
i
An index over a single space variable, usually .
ix, iy, iz
Indices over two or three space variables, , , and , respectively.
k
An index iterating over a time variable.
M
A matrix.
m
Either the row-dimension of a matrix M (an m × n matrix) or an index of a vector.
n
Either the column-dimension of a matrix M (an m × n matrix) or a positive integer indicating the number of points into which an interval will be divided.
N_max
A maximum number of steps or iterations.
t_out
An output column vector indicating the partition of a time interval .
t_rng
A time interval where , that is, from an initial time to a final time .
x_rng
A space interval over a variable where .
u0
The initial values (a vector) of -values where usually U_out(1,:) = u0 for a solution over time and a single space variable .
U0
The initial values (a 2- or 3-dimensional array) of -values where usually U_out(1,:,:) = U0 or U_out(1,:,:,:) = U0 for a solution over time and two or three space variables , , and .
u_out
An output column vector of -values where usually y_out(1,:) = y0 for a solution over time.
U_out
An output column vector of -values where usually y_out(1,:) = y0 for a solution over time.
y0
An initial value (either a scalar or a column vector) of -values where usually y_out(1,:) = y0 for a solution over time.
y_out
An output column vector of -values where usually y_out(1,:) = y0 for a solution over time.