The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method

<table>Exact solution and 20th order approximation for <svg height="12.4375" id="M254" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.8999996 12.4375" width="8.8999996" 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)"><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>
</svg> = −0,64.</table>

Mathematical Problems in Engineering

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Figure 8

Figure 8: The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method 