A Review of Some Recent Results for the Approximate Analytical Solutions of Nonlinear Differential Equations

<table>Approximate solutions to the system (<a href="https://static.hindawi.com/articles/mpe/volume-2009/202307/figures/#EEq1.5">1.7</a>) by Adomian's decomposition method with <svg height="10.85" id="M620" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 36.137501 10.85" width="36.137501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.85)">
<g transform="translate(72,-63.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.45" id="M621" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 64.675003 13.45" width="64.675003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑢</tspan>
<tspan style="font-size: 12.50px; " x="5.9264221" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.089921" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="16.341421" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="23.96825" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="36.00864" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="42.260139" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="45.385891" y="0">3</tspan>
</text>
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</g>
</svg>, <svg height="13.575" id="M622" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 65.175003 13.575" width="65.175003" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-61.14)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑣</tspan>
<tspan style="font-size: 12.50px; " x="6.3265181" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.490017" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="16.741516" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="24.368347" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="36.408737" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="42.660236" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="45.785988" y="0">6</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: A Review of Some Recent Results for the Approximate Analytical Solutions of Nonlinear Differential Equations 