Chebyshev function definition

@CHEBYSHEV_POLYNOMIAL_FUNCTION {
@CHEBYSHEV_POLYNOMIAL_NAME {ChbFunName} {
@FUNCTION_1D_TYPE {Fun1DType}
@APPROXIMATION_RANGE {xlo, xhi}
@CHEBYSHEV_COEFFICIENTS {c1, c2,..., cN}
@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

  1. 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.
  2. Chebyshev functions are defined by the following data.
    • The lower and upper bounds of the approximation, denoted xlo and xhi, 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, c1, c2,... , cN.
  3. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.