New Approximate Analytical Solutions of the Falkner-Skan Equation

<table>The Adomian solutions <svg height="20.6625" id="M104" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 40.575001 20.6625" width="40.575001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.162)"><use xlink:href="#x1D466"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.9,8)"><use xlink:href="#x1D434"></use></g><g transform="matrix(.012,-0,0,-.012,9.9,20.238)"><use xlink:href="#x1D45B"></use></g>
<g transform="matrix(.017,-0,0,-.017,19.25,16.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,25.132,16.162)"><use xlink:href="#x1D465"></use></g><g transform="matrix(.017,-0,0,-.017,34.634,16.162)"><use xlink:href="#x29"></use></g>
</svg> and their errors in (a) and presented solutions <svg height="16.625" id="M105" 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) for the Falkner-Skan equation with <svg height="16.6625" id="M106" 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)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>.</table>

Journal of Applied Mathematics

New Approximate Analytical Solutions of the Falkner-Skan Equation

Figure 3