Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag

<table>Accuracy (Digits) for several values of CPU Time (in Seconds) for the eigenvalue <svg height="14.875" id="M176" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 111 14.875" width="111" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.875)">
<g transform="translate(72,-60.1)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.02,60.27)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
<text transform="matrix(1,0,0,-1,-54.68,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="24.543388" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="30.794889" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="33.920639" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="40.172138" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="46.423637" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="52.67514" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="58.92664" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="65.178139" y="0">6</tspan>
</text>
</g>
</g>
</svg>. The nonexistence of a value of Accuracy (Digits) indicates that for this value of CPU, Accuracy (Digits) is less than 0.</table>

Journal of Applied Mathematics

fig5

Figure 5

Figure 5: Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag 