## Applied numerical methodsInterpolation and approximation; Numerical integration; Solution of equations; Matrices and related topics; Systems of equations; The approximation of the solution of ordinary differential equations; Approximation of the solution of partial differential equations; Statistical methods. |

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algorithm approximation argument assumed augmented matrix base points Bernoulli's method calculations Chebyshev polynomials coefficient matrix column Computer Output Continued constant convergence corrector corresponding Data Set derivative determinant diagonal distribution divided differences divided-difference eigenvalues eigenvectors EPS1 EPS2 error term estimate Euler's method evaluate example Figure finite-difference FORTRAN functional values Gauss-Legendre quadrature Gauss-Seidel method given heat IDEG initial conditions interpolating polynomial interval IPRINT ITMAX linear equations magnitude main program maximum mole Newton's nomial number of iterations o o o o o o ordinary differential equations orthogonal PARAMETERS pn(x polynomial of degree PRINT procedure Program Listing Continued quadrature formula respectively roots round-off error Runge-Kutta Runge-Kutta method Section sequence shown in Fig Simpson's rule solved step subroutine subscripts Table temperature tion transformation trapezoidal rule truncation error vector velocity weight factors Write a program XARG XMAX zero