A Third-Order <svg     style="vertical-align:-4.626pt;width:13.4125px;" id="M1" height="17.5" version="1.1" viewBox="0 0 13.4125 17.5" width="13.4125"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg>-Laplacian Boundary Value Problem Solved by an SL<svg     style="vertical-align:-3.06pt;width:51.849998px;" id="M2" height="19.85" version="1.1" viewBox="0 0 51.849998 19.85" width="51.849998"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> Lie-Group Shooting Method

<table>Example <a href="https://static.hindawi.com/articles/jam/volume-2013/497863/figures/#ex3">3</a> comparing the first numerical solution and the second numerical solution with the exact solution.</table>

Journal of Applied Mathematics

fig6

Figure 6

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			<g transform="matrix(.022,-0,0,-.022,.062,11.675)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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</svg>-Laplacian Boundary Value Problem Solved by an SL<svg     style="vertical-align:-3.06pt;width:51.849998px;" id="M2" height="19.85" version="1.1" viewBox="0 0 51.849998 19.85" width="51.849998"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g><g transform="matrix(.022,-0,0,-.022,18.578,15.975)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.022,-0,0,-.022,27.41,15.975)"><path id="x211D" d="M751 18q-1 -4 -2 -13t-2 -13q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -62 14 -77t74 -20v-28h-382v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h372q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172
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</svg> Lie-Group Shooting Method 

Journal of Applied Mathematics

A Third-Order -Laplacian Boundary Value Problem Solved by an SL Lie-Group Shooting Method

Figure 6