## Introduction to numerical analysis |

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A Good Book on Numerical Analysis

### Contents

Errors in Numerical Computations | 1 |

Polynomial Approximations and Finite Differences | 41 |

Numerical Integration | 59 |

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abscissas Af(x augmented matrix calculated chapter coefﬁcients corrector deﬁned in Equation degree 2m derivative determine diagonal difference table differential equation difﬁcult digital computer discussed error analysis error term EXAMPLE Exercises factorial polynomials ﬁnal ﬁnding ﬁnite ﬁrst approximation ﬁt formula to ﬁnd function f Gauss-Seidel method Gaussian quadrature given by Equation gives Gregory-Newton polynomial Hence Hermite interpolation Hermite interpolation formula Hilbert matrix initial condition interval xo iteration method least-squares polynomial Legendre polynomials mation method of false multiplication Newton-Cotes formulas Newton—Raphson Numerical Analysis numerical solution obtained orthogonal polynomials places of accuracy polynomial of degree powers of h Property real root reduced remainder term Repeat Problem replaced result round-off error Runge-Kutta method satisﬁed set of equations Show solved speciﬁed step subintervals synthetic division Taylor’s series Theorem trapezoidal rule truncation error upper bound variables zero