Residuals define the system of equations, typically by using derivative operators.
Assuming the proper definitions of the derivative operators, this residual will encodes the linear wave equation on a string with the end points fixed. First comes the reserved word residual followed by the name of the grid function whose residual is being defined. Next comes a bracket-enclosed set of index regions and expressions. The index region shows over what range the expression is a valid description of the behavior of the system. The union of the index regions should equal the index region of the grid on which the function is defined, but this is not required.