beam.c running E=10, I=9, W=7, L=8, h=1, n=9 Analytic Solution. beam x=0, y=-0 slope=0 beam x=1, y=-0.0198495 slope=-0.0340278 beam x=2, y=-0.0583333 slope=-0.0388889 beam x=3, y=-0.0911458 slope=-0.0243056 beam x=4, y=-0.103704 slope=1.92747e-20 beam x=5, y=-0.0911458 slope=0.0243056 beam x=6, y=-0.0583333 slope=0.0388889 beam x=7, y=-0.0198495 slope=0.0340278 beam x=8, y=-0 slope=3.85494e-20 Numerical Solution. Runge-Kutta 4th order solution not valid because boundary conditions at end not used x y slope 0.000000 0.000000 0.000000 0.125000 -0.000737 -0.005895 0.250000 -0.002140 -0.011228 0.375000 -0.004143 -0.016024 0.500000 -0.006682 -0.020312 0.625000 -0.009698 -0.024124 0.750000 -0.013134 -0.027491 0.875000 -0.016941 -0.030450 1.000000 -0.021070 -0.033039 1.125000 -0.025483 -0.035298 1.250000 -0.030141 -0.037269 1.375000 -0.035016 -0.038999 1.500000 -0.040083 -0.040534 1.625000 -0.045323 -0.041924 1.750000 -0.050726 -0.043221 1.875000 -0.056286 -0.044481 2.000000 -0.062006 -0.045760 2.125000 -0.067896 -0.047117 2.250000 -0.073972 -0.048613 2.375000 -0.080262 -0.050315 2.500000 -0.086797 -0.052286 2.625000 -0.093622 -0.054597 2.750000 -0.100787 -0.057319 2.875000 -0.108353 -0.060525 3.000000 -0.116389 -0.064291 3.125000 -0.124976 -0.068696 3.250000 -0.134203 -0.073819 3.375000 -0.144172 -0.079745 3.500000 -0.154991 -0.086559 3.625000 -0.166785 -0.094349 3.750000 -0.179685 -0.103204 3.875000 -0.193838 -0.113217 4.000000 -0.209398 -0.124484 4.125000 -0.226536 -0.137101 4.250000 -0.245432 -0.151168 4.375000 -0.266280 -0.166788 4.500000 -0.289288 -0.184065 4.625000 -0.314676 -0.203105 4.750000 -0.342679 -0.224018 4.875000 -0.373543 -0.246915 5.000000 -0.407532 -0.271910 5.125000 -0.444922 -0.299121 5.250000 -0.486005 -0.328664 5.375000 -0.531088 -0.360661 5.500000 -0.580492 -0.395237 5.625000 -0.634557 -0.432515 5.750000 -0.693635 -0.472626 5.875000 -0.758097 -0.515699 6.000000 -0.828330 -0.561867 6.125000 -0.904739 -0.611265 6.250000 -0.987743 -0.664031 6.375000 -1.077781 -0.720306 6.500000 -1.175310 -0.780231 6.625000 -1.280804 -0.843952 6.750000 -1.394756 -0.911615 6.875000 -1.517677 -0.983370 7.000000 -1.650098 -1.059369 7.125000 -1.792569 -1.139767 7.250000 -1.945659 -1.224719 7.375000 -2.109957 -1.314385 7.500000 -2.286073 -1.408927 7.625000 -2.474636 -1.508508 7.750000 -2.676298 -1.613294 7.875000 -2.891730 -1.723454 8.000000 -3.121625 -1.839158 Fourth order difference equation solution inaccurate because boundary dy/dx=0 used for inner points n=61, h=0.125, C={1,-4,6,-4,1} x=0, y=0 boundary x=0.125, y=0 boundary x=0.25, y=-0.000748076 x=0.375, y=-0.00217183 x=0.5, y=-0.00420125 x=0.625, y=-0.00676869 x=0.75, y=-0.00980886 x=0.875, y=-0.0132589 x=1, y=-0.0170582 x=1.125, y=-0.0211487 x=1.25, y=-0.0254745 x=1.375, y=-0.0299824 x=1.5, y=-0.0346212 x=1.625, y=-0.0393422 x=1.75, y=-0.0440993 x=1.875, y=-0.0488485 x=2, y=-0.0535482 x=2.125, y=-0.0581593 x=2.25, y=-0.062645 x=2.375, y=-0.0669708 x=2.5, y=-0.0711048 x=2.625, y=-0.0750173 x=2.75, y=-0.0786809 x=2.875, y=-0.0820708 x=3, y=-0.0851644 x=3.125, y=-0.0879415 x=3.25, y=-0.0903843 x=3.375, y=-0.0924774 x=3.5, y=-0.0942078 x=3.625, y=-0.0955647 x=3.75, y=-0.0965398 x=3.875, y=-0.0971273 x=4, y=-0.0973235 x=4.125, y=-0.0971273 x=4.25, y=-0.0965398 x=4.375, y=-0.0955647 x=4.5, y=-0.0942078 x=4.625, y=-0.0924774 x=4.75, y=-0.0903843 x=4.875, y=-0.0879415 x=5, y=-0.0851644 x=5.125, y=-0.0820708 x=5.25, y=-0.0786809 x=5.375, y=-0.0750173 x=5.5, y=-0.0711048 x=5.625, y=-0.0669708 x=5.75, y=-0.062645 x=5.875, y=-0.0581593 x=6, y=-0.0535482 x=6.125, y=-0.0488485 x=6.25, y=-0.0440993 x=6.375, y=-0.0393422 x=6.5, y=-0.0346212 x=6.625, y=-0.0299824 x=6.75, y=-0.0254745 x=6.875, y=-0.0211487 x=7, y=-0.0170582 x=7.125, y=-0.0132589 x=7.25, y=-0.00980886 x=7.375, y=-0.00676869 x=7.5, y=-0.00420125 x=7.625, y=-0.00217183 x=7.75, y=-0.000748076 x=7.875, y=0 boundary x=8, y=0 boundary