Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations

<table>Solutions of (<a href="https://static.hindawi.com/articles/ddns/volume-2012/365792/figures/#EEq20">4.8</a>) and (<a href="https://static.hindawi.com/articles/ddns/volume-2012/365792/figures/#EEq21">4.9</a>). Dotted line: the 5th-order approximate HAM solution at  <svg height="12.4375" id="M197" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 46.450001 12.4375" width="46.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.163)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l112 522h-84l11 39h81l7 33q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-25 -117h165
l-12 -39h-161l-55 -261h2q77 102 195 167q44 24 79 24q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210F"></path></g><g transform="matrix(.017,0,0,-.017,13.543,12.163)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,0,0,-.017,28.246,12.163)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,0,0,-.017,38.225,12.163)"><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> and solid line: the exact solution.</table>

Discrete Dynamics in Nature and Society

fig6

Figure 6

Figure 6: Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations 