Chebyshev function definition
- @CHEBYSHEV_POLYNOMIAL_FUNCTION {
- @CHEBYSHEV_POLYNOMIAL_NAME {ChbFunName} {
- @FUNCTION_1D_TYPE {Fun1DType}
- @APPROXIMATION_RANGE {x_{lo}, x_{hi}}
- @CHEBYSHEV_COEFFICIENTS {c_{1}, c_{2},..., c_{N}}
- @COMMENTS {CommentText}
- }
- }
Introduction
The Chebyshev function describes an arbitrary function of a single variable, F = F(x), where x is the independent variable and F the value of the function, by its expansion in terms of Chebyshev polynomials. Chebyshev functions are used in conjunction with 1D functions. A plot of the function will be generated if plotting control parameters are defined.
NOTES
- The nature of the data entered in the Chebyshev function is determined by parameter Fun1DType.
- Possible values of parameter Fun1DType are listed for the associated 1D function.
- Parameters Fun1DType defined for the Chebyshev function and associated 1D function must match.
- Parameter Fun1DType defines the units of the independent variable, x, and of Chebyshev function F.
- Chebyshev functions are defined by the following data.
- The lower and upper bounds of the approximation, denoted x_{lo} and x_{hi}, respectively, define the range over which the approximation is valid. If independent variable x falls outside this range during the simulation, a warning message will be printed. As explained in the discussion of Chebyshev polynomials, the coefficients of the expansion depend on the he range over which the approximation is defined.
- The N coefficients of Chebyshev's polynomial expansion, c_{1}, c_{2},... , c_{N}.
- It is possible to attach comments to the definition of the object; these comments have no effect on its definition.