{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gauss quadrature of sqrt(x-0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us compute\n",
"$$\n",
"\\int_0^1 \\sqrt{|x-1/2|} dx = \\frac{\\sqrt{2}}{3}\n",
"$$\n",
"We will compute this with Gauss-Legendre quadrature and also by breaking it into two parts\n",
"$$\n",
"\\int_0^{1/2} \\sqrt{|x-1/2|} dx + \\int_{1/2}^1 \\sqrt{|x-1/2|} dx\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 2 6.588045e-02 0.0000e+00 2.859548e-02 0.0000e+00\n",
" 4 2.572864e-02 2.5606e+00 5.105786e-03 5.6006e+00\n",
" 8 9.738642e-03 2.6419e+00 8.209359e-04 6.2195e+00\n",
" 16 3.583266e-03 2.7178e+00 1.194398e-04 6.8732e+00\n",
" 32 1.294540e-03 2.7680e+00 1.623859e-05 7.3553e+00\n",
" 64 4.628656e-04 2.7968e+00 2.121816e-06 7.6532e+00\n",
" 128 1.645897e-04 2.8122e+00 2.713392e-07 7.8198e+00\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
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"text/plain": [
"