az Consider the integral /= f(6x + 3x²)dx: Approximate I with the values Q, and Q₂ obtained from Cavalieri-Simpson initially applied over the full interval and then over two equal sub-intervals. Approximates then / using Richardson's extrapolation (R); Approximate I with the value T₁ obtained from the trapezoidal rule with n = 4 equal subdivisions of the integration interval; estimate un upper bound (theoretical) Emax of the error made using the trapezoidal rule; pute / analytically and the exact errors F F
az Consider the integral /= f(6x + 3x²)dx: Approximate I with the values Q, and Q₂ obtained from Cavalieri-Simpson initially applied over the full interval and then over two equal sub-intervals. Approximates then / using Richardson's extrapolation (R); Approximate I with the value T₁ obtained from the trapezoidal rule with n = 4 equal subdivisions of the integration interval; estimate un upper bound (theoretical) Emax of the error made using the trapezoidal rule; pute / analytically and the exact errors F F
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the integral /= f(6x + 3x²)dx:
Approximate I with the values Q, and Q₂ obtained from Cavalieri-Simpson initially applied
over the full interval and then over two equal sub-intervals. Approximates then / using
Richardson's extrapolation (R);
Approximate I with the value T₁ obtained from the trapezoidal rule with n = 4 equal
subdivisions of the integration interval; estimate un upper bound (theoretical) Emax of the
error made using the trapezoidal rule;
& Compute I analytically and the exact errors E, and E₂ made by Richardson and the trapezoidal
rule, respectively.
Write the results in the following table:
Q₁
7
Q₂
R
T₁
R
Emax
az
E₁
E₂
3. Derive the convergence conditions of the iterative scheme Xk+1= Ex + q for the solution of
the system. Ax = b. Discuss the Jacobi, Gauss-Seidel and over-relaxation schemes and the
respective convergence properties.
NB: Failing to complete the tables is recognizing that the exercises are not done
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