A Shannon-Runge-Kutta-Gill Method for Convection-Diffusion Equations

<table>Shannon scaling function <svg height="12.325" id="M6" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 10.0125 12.325" width="10.0125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.825)"><path d="M559 271q0 -109 -83 -187t-189 -89l-36 -213q-16 -30 -86 -43l-7 9q10 36 53 242q-91 11 -139.5 63.5t-48.5 132.5q0 186 242 271l11 -28q-76 -34 -119.5 -91.5t-43.5 -136.5q0 -66 29 -108.5t77 -55.5q39 205 56 260q21 71 65 111t93 40q50 0 88 -45.5t38 -131.5z
M484 273q0 65 -26.5 99t-52.5 34q-37 0 -53 -75l-59 -298q80 5 135.5 74.5t55.5 165.5z" id="x1D711"></path></g>
</svg> and mother function <svg height="13.225" id="M7" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 11.2375 13.225" width="11.2375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.737)"><path d="M642 419q-50 -36 -71 -94q-28 -78 -68 -170q-39 -89 -114 -135q-34 -21 -83 -31l-45 -219l-31 -31q-8 7 -15 29.5t-2 45.5l35 172q-153 10 -153 169q0 28 6 84q7 68 7 88q0 48 -27 48q-18 0 -51 -28l-7 26q62 75 118 75q49 0 49 -90q0 -47 -5 -81q-10 -72 -10 -108
q0 -117 82 -133l87 455l62 19l7 -2l-99 -478q91 12 131 120q34 93 51 154q20 73 36 88q42 40 103 56z" id="x1D713"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

A Shannon-Runge-Kutta-Gill Method for Convection-Diffusion Equations

Figure 1