New Approximate Analytical Solutions of the Falkner-Skan Equation

<table>Truncated Blasius series <svg height="16.4125" id="M73" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 36.150002 16.4125" width="36.150002" 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="#x1D446"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.225,16.212)"><use xlink:href="#x1D45B"></use></g>
<g transform="matrix(.017,-0,0,-.017,14.813,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,20.694,12.138)"><use xlink:href="#x1D465"></use></g><g transform="matrix(.017,-0,0,-.017,30.196,12.138)"><use xlink:href="#x29"></use></g>
</svg> and their errors in (a) and presented solutions <svg height="16.625" id="M74" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 37.825001 16.625" 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,.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(.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> and their errors in (b), <svg height="13.0125" id="M75" style="vertical-align:-1.59705pt" version="1.1" viewbox="0 0 95.712502 13.0125" width="95.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.963)"><use xlink:href="#x1D45B"></use></g><g transform="matrix(.017,-0,0,-.017,13.305,10.963)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,28.008,10.963)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,36.168,10.963)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,42.882,10.963)"><use xlink:href="#x33"></use></g><g transform="matrix(.017,-0,0,-.017,51.042,10.963)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,57.739,10.963)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,65.899,10.963)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,72.613,10.963)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,80.773,10.963)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,87.487,10.963)"><use xlink:href="#x36"></use></g>
</svg>, for the Blasius equation (<svg height="16.6625" id="M76" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 37.587502 16.6625" width="37.587502" 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>
</svg>).</table>

Journal of Applied Mathematics

New Approximate Analytical Solutions of the Falkner-Skan Equation

Figure 1