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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.CR: Chapter 8 Review
Problem 11CR
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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
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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