## Numerical analysis |

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accuracy Adams-Moulton Adaptive Quadrature Algorithm applied approximate the solution arithmetic boundary conditions calculations coefficients Compute consider constant convergence cubic spline defined Definition denoted derivatives determine differential equation eigenvalues entries error bound error term Euler's method evaluating EXAMPLE Exercise Set find an approximation fixed point fourth-order function Gaussian elimination Gaussian quadrature given gives implies initial approximation initial-value problem integral Intermediate Value Theorem interpolating polynomial interval involved Lagrange polynomial linear system Lipschitz condition matrix maximum number method of order multistep method Newton-Cotes formulas Newton's method nodes notation number of iterations obtained in Exercise polynomial of degree proof quadratic real numbers Repeat Exercise root rounding errors Runge-Kutta method Secant method Section sequence Show Simpson's composite rule Simpson's rule solve Step 1 Set subintervals Suppose Table Taylor polynomial technique trapezoidal rule truncation error unique solution Value Theorem vector wi+1