Application of the Homotopy Perturbation Method for Solving the Foam Drainage Equation

<table>The absolute error of HPM at <svg height="10.9125" id="M49" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 51.75 10.9125" width="51.75" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑡</tspan>
<tspan style="font-size: 12.50px; " x="7.37677" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="19.417158" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="25.668659" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="28.794409" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="35.04591" y="0">1</tspan>
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</svg> (a) <svg height="10.8625" id="M50" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 33.8125 10.8625" width="33.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8625)">
<g transform="translate(72,-63.31)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="8.6520758" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.692465" y="0">1</tspan>
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</svg> (b) <svg height="10.8625" id="M51" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 33.8125 10.8625" width="33.8125" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-63.31)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="8.6520758" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.692465" y="0">2</tspan>
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</svg>.</table>

International Journal of Differential Equations

fig5

Figure 5

Figure 5: Application of the Homotopy Perturbation Method for Solving the Foam Drainage Equation 