Grid

The equations of example_pkg.grid, declared on the code that implements them and checked by the tests.

midpoint_integral

functionsource

The integral of f on [start, stop] by the composite midpoint rule.

rule

$$\int_a^b f(x)\,dx \approx h \sum_{i=0}^{n-1} f\left(\frac{x_i + x_{i+1}}{2}\right)$$

error

$$\left|E\right| \le \frac{(b - a) h^2}{24} \max_{[a, b]} |f''|$$

Order

2

Assumes

• f twice continuously differentiable on [a, b]

References

• Süli and Mayers, An Introduction to Numerical Analysis (2003), section 7.2