Compute . dx using the (a) Trapezoidal rule (b) Trapezoidal rule with end corrections using the first derivative (c) Trapezoidal rule with end corrections using the first derivative and third derivatives (d) Gauss-Legendre quadrature

Compute . dx using the (a) Trapezoidal rule (b) Trapezoidal rule with end corrections using the first derivative (c) Trapezoidal rule with end corrections using the first derivative and third derivatives (d) Gauss-Legendre quadrature

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

For n=5

C part only

Compute
'dx using the
-1
(a) Trapezoidal rule
(b) Trapezoidal rule with end corrections using the first derivative
(c) Trapezoidal rule with end corrections using the first derivative and third derivatives
(d) Gauss-Legendre quadrature
• Perform this by subdividing [-1, 1] into NE {2,5, 10, 20, 50, 100} panels

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