New Approximate Analytical Solutions of the Falkner-Skan Equation

<table>Absolute errors of the presented solutions <svg height="16.625" id="M251" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 50.525002 16.625" width="50.525002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D466"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.9,16.213)"><use xlink:href="#x1D45B"></use></g><g transform="matrix(.012,-0,0,-.012,15.873,16.213)"><use xlink:href="#x2B"></use></g><g transform="matrix(.012,-0,0,-.012,22.858,16.213)"><use xlink:href="#x31"></use></g>
<g transform="matrix(.017,-0,0,-.017,29.2,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,35.082,12.138)"><use xlink:href="#x1D465"></use></g><g transform="matrix(.017,-0,0,-.017,44.584,12.138)"><use xlink:href="#x29"></use></g>
</svg> (thin lines) and those of the corrected solutions <svg height="17.625" id="M252" style="vertical-align:-4.3598pt" version="1.1" viewbox="0 0 37.825001 17.625" width="37.825001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,2.525,12.138)"><use xlink:href="#xF5C01"></use></g><g transform="matrix(.017,-0,0,-.017,.077,12.138)"><use xlink:href="#x1D466"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.9,17.412)"><use xlink:href="#x1D45B"></use></g>
<g transform="matrix(.017,-0,0,-.017,16.5,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,22.382,12.138)"><use xlink:href="#x1D465"></use></g><g transform="matrix(.017,-0,0,-.017,31.884,12.138)"><use xlink:href="#x29"></use></g>
</svg> (thick lines) for <svg height="16.6625" id="M253" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 109.525 16.6625" width="109.525" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D6FD"></use></g><g transform="matrix(.017,-0,0,-.017,14.647,12.162)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,29.351,12.162)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,37.511,12.162)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,41.386,12.162)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,49.546,12.162)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,56.26,12.162)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,64.42,12.162)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,71.117,12.162)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,81.096,12.162)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,89.255,12.162)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,93.131,12.162)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,101.29,12.162)"><use xlink:href="#x34"></use></g>
</svg>.</table>

Journal of Applied Mathematics

New Approximate Analytical Solutions of the Falkner-Skan Equation

Figure 7