Euler's method for numerical solution of a first order DEedited for E&P problem 2.4.1 b) n = 5 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NiI=Edwards and Penney 3rd Edition Project 2.4
[described in textbook section 2.4 Application pp.123--124]
Disclaimer: This is really just a tease to expose you to the idea of numerically approximating DEs.
It is also an example of seeing some Maple programming code that is relatively simple to follow, but easier to modify to apply to other similar problems (only the red commented lines need be edited). For your Maple homework, another file can be used with only the part you need execute.introducing the algorithm (you can use this part to do the textbook homework problem if you like)Here is the DE we want to solve numerically and exactly to compare:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Iy1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRis=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Here are the initial values LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYlUSN4MEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEjeTBGJ0Y0RjdGPkY+LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj4= of the two variables and the final value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn of the first variable defining the interval LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjeDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSYmbGVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRInhGJ0YvRjJGNS1GLDYlUSN4ZkYnRi9GMkY5 over which we want to solve the DE with an initial condition at the left endpoint: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Here is the number of subintervals and resulting stepsize:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JUYrLUYjNiUtRiw2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtSSNtbkdGJDYkUSI1RidGQEYrLUY9Ni1RIjtGJ0ZARkIvRkZGOEZHRklGS0ZNRk8vRlJRJjAuMGVtRidGVC1GPTYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZCRkVGR0ZJRktGTUZPRmhuL0ZVRmluLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2MFEiI0YnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZLLUkjbWlHRiQ2KFFib35lZGl0fnRoaXN+bGluZX50b35yZXVzZX5mb3J+ZGlmZmVyZW50fnByb2JsZW1+b3J+c2ltcGx5fm1vcmV+ZGl2aXNpb25zRidGLy8lJ2l0YWxpY0dGMUYyL0Y2USxib2xkLWl0YWxpY0YnRjgtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGSy8lJmRlcHRoR0Zlbi8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GVzYmRllGZm5GaG4vRltvUSVhdXRvRictRk82JVEiaEYnRlIvRjZRJ2l0YWxpY0YnLUYsNi1RKiZjb2xvbmVxO0YnL0Y2USdub3JtYWxGJ0Y6Rj1GP0ZBRkNGRUZHL0ZKUSwwLjI3Nzc3NzhlbUYnL0ZNRlxwLUZPNiVRJmV2YWxmRidGUkZkby1JKG1mZW5jZWRHRiQ2JC1GIzYlLUZPNiNRIUYnLUkmbWZyYWNHRiQ2KC1GIzYlRmZwLUYjNiUtRk82JVEjeGZGJ0ZSRmRvLUYsNi1RKCZtaW51cztGJ0Zpb0Y6Rj1GP0ZBRkNGRUZHL0ZKUSwwLjIyMjIyMjJlbUYnL0ZNRmdxLUZPNiVRI3gwRidGUkZkb0ZmcC1GIzYjLUZPNiVRIm5GJ0ZSRmRvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zmci8lKWJldmVsbGVkR0Y8RmZwRmlvNow we step by step build up our routine.
We first initialize our two variables:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JUYrLUYjNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiw2JVEjeDBGJ0Y2RjlGKy1GPTYtUSI7RidGQEZCL0ZGRjhGR0ZJRktGTUZPL0ZSUSYwLjBlbUYnRlQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUSN5MEYnRjRGN0Yrand do a loop to iterate the procedure n times (the code is almost self-explanatory, but is documented):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Since we are using LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as a discrete variables, we cannot use them in stating and solving the DE exactly so we use the uppercase letters to compare with the exact solution final value: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 can now compare with the exact value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiNRIUYnLUYjNigtRiw2JVEjWVlGJ0YvRjJGNS1GUDYkLUYjNiYtRiw2JVEieEYnRi9GMi8lK2V4ZWN1dGFibGVHRjEvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjlGOUZdb0Zfb0Y5RlRGXW9GX29GOUY5Rl1vRl9vRjk= at each step:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEjeDBGJ0YvRjItRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZZLUYsNiVRInlGJ0YvRjJGNS1GLDYlUSN5MEYnRi9GMkZSLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlkvJSZkZXB0aEdGYG8vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2I1EhRictRiM2MUZoby1GIzYlLUYsNiVRJnByaW50RidGL0YyLUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZYRlotSShtZmVuY2VkR0YkNiQtRiM2J0Zoby1GIzYlLUYsNiVRJmV2YWxmRidGL0YyRmJwLUZmcDYkLUYjNiNGT0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGWC9GTlEsMC4zMzMzMzMzZW1GJy1GIzYlRlxxRmJwLUZmcDYkLUYjNiNGaG5GOUZob0Y5LUY2Ni1RIjtGJ0Y5RjtGZnFGQEZCRkRGRkZIRlhGTUZVLUY2Ni1RIiNGJ0Y5RjtGPkZARkJGREZGRkhGSkZNRlUtRiw2JlEjdG9GJ0YvLyUrZm9yZWdyb3VuZEdRLFsyNTUsMCwyNTVdRidGMkZVLUYsNiZRJHNlZUYnRi9GaHJGMkZVLUYsNiZRJHRoZUYnRi9GaHJGMkZVLUYsNiZRKXN0YXJ0aW5nRidGL0ZockYyRlUtRiw2JlEmcG9pbnRGJ0YvRmhyRjJGaG9GW29GaG8tRiM2XnQtRiw2JVEkZm9yRidGL0YyRlUtRiw2JVEiaUYnRi9GMkZVLUYsNiVRJWZyb21GJ0YvRjJGVS1JI21uR0YkNiRRIjFGJ0Y5RlUtRiw2JUZnckYvRjJGVS1GLDYlUSJuRidGL0YyRlUtRiw2JVEjZG9GJ0YvRjJGW29GVUZVLUYsNiVRImtGJ0YvRjJGNS1GIzYlLUYsNiVRImZGJ0YvRjJGYnAtRmZwNiQtRiM2JUYrRmNxRmVuRjlGUkZVRlVGVUZVRmJyRlVGXnNGVS1GLDYmUSZzbG9wZUYnRi9GaHJGMkZVLUYsNiZGW3RGL0ZockYyRlVGXnNGVS1GLDYmUSVzdGVwRidGL0ZockYyRlUtRiw2JlEjYXRGJ0YvRmhyRjJGVUZec0ZVLUYsNiZRJWxlZnRGJ0YvRmhyRjJGVS1GLDYmUSllbmRwb2ludEYnRi9GaHJGMkZVLUYsNiZRI29mRidGL0ZockYyRlVGXnNGVS1GLDYmUSlpbnRlcnZhbEYnRi9GaHJGMkZbb0ZVRlVGVUZlbkY1RmVuLUY2Ni1RJyZwbHVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZldy1GLDYlUSJoRidGL0YyRlVGXnVGX3JGVUZVRmJyRlUtRiw2JlEmRXVsZXJGJ0YvRmhyRjJGVUZfdkZVRmVyRlUtRiw2JlEndXBkYXRlRidGL0ZockYyRlUtRiw2JkZnbkYvRmhyRjJGVS1GLDYmUSZhbG9uZ0YnRi9GaHJGMkZVLUYsNiZRKGluaXRpYWxGJ0YvRmhyRjJGVS1GLDYmUSh0YW5nZW50RidGL0ZockYyRlUtRiw2JlElbGluZUYnRi9GaHJGMkZbb0ZVRlVGVUYrRjVGK0Zhd0Znd0ZfckZVRlVGVUZVRlVGVUZVLUY2Ni1GZHJGOUY7RmZxRkBGQkZERkZGSEZYRmdxRlVGVUZdeEZVLUYsNiZGLkYvRmhyRjJGVUZlckZVLUYsNiZRJnJpZ2h0RidGL0ZockYyRlVGaHZGVUZbd0ZVRl53RltvRlVGVUZVLUYjNjFGX3BGYnAtRjY2LVEiKEYnRjkvRjxGMUY+L0ZBRjFGQkZERkZGSC9GS1EsMC4xNjY2NjY3ZW1GJy9GTlEsMC4xMTExMTExZW1GJ0YrRmNxRmVuRmNxRlxxRmJwLUZmcDYkLUYjNiVGaG8tRiM2JS1GLDYlUSNZWUYnRi9GMkZicC1GZnA2JC1GIzYjLUYsNiZGLkYvLyUrZXhlY3V0YWJsZUdGPUYyRjlGaG9GOUZoby1GNjYtUSIpRidGOUZqeUY+Rlt6RkJGREZGRkhGXHpGXnpGaG8tRiM2I0Zob0Zob0ZVRlVGVUZVRlVGYnJGVUZVLUYsNiZGYXBGL0ZockYyRlUtRiw2JlEoY3VycmVudEYnRi9GaHJGMkZVLUYsNiZRJ3ZhbHVlc0YnRi9GaHJGMkZVLUYsNiZRJGFuZEYnRi9GaHJGMkZVLUYsNiZRJmV4YWN0RidGL0ZockYyRlUtRiw2JlEmdmFsdWVGJ0YvRmhyRjJGVUZbd0ZVRmB4RltvLUYsNiVRI29kRidGL0YyRlJGVQ==We can also move the print step to after the loop to only print the final values and also print the error and the values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= so we can compare results for different values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. We collect all the initializations together to make a single unit of the procedure:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JUYrLUYjNiUtRiw2JVEjeDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUkjbW5HRiQ2JFEiMEYnRkBGKy1GPTYtUSI7RidGQEZCL0ZGRjhGR0ZJRktGTUZPL0ZSUSYwLjBlbUYnRlQ=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 the first pair is iteration number LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== , and stepsize h ,
the second pair is the numerical solution endpoint values of the two variables LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ,
the next one is the exact endpoint value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=,
then the actual error, which is negative if the approximate solution drops below the exact solution as in the example (concave up curve).visualize itSince the solution curve is concave up, the tangent lines are always below the curve, so this piecewise straight line solution will lag below the actual solution, getting farther away with each step: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saving the Eulerpoints to add to graph (no need to understand this detour)We redo the loop capturing the successive points in a list that we can plot together with this directionfield and solution curve.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Notice how the error grows.using it to examine how the error depends on the stepsize [ignore this or continue editing here]Use this to do the famous number investigation on the first page (page 38) of Project 2.4, parts 1 and 2 for e and 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, also described on pages 123-124 in your textbook, and on our Maple homework page from which you got this file.
For each of these two investigations, record your results by copying the output line for each choice of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and pasting into a new input line with a semicolon at the end, adding each new result in the same input region after a shift enter to get a new line within it (MAPLE input mode, not Math Notation Mode). Executing the final input will produce the blue output table. As you half the stepsize, how does the percentage error go down approximately? What value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is needed to get---twice in succession---the correct value of the target number rounded off to 3 decimal places?
[Answer these questions with MAPLE comments. Put each of these two edited problems in their own separate subsections labeled 1 and 2. EDIT away these instructions. The input lines which require editing for a new DE and initial and final conditions, or to change the iteration number, are marked by # EDIT.]
Of course one has to also redefine the differential equation and exact solution, so one has to package this together with the other block to get everything in one place so one can redo this for a new DE: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QyUvSSN5Zkc2Ii1JJmV2YWxmRyUqcHJvdGVjdGVkRzYjLUkjWVlHRiU2I0kjeGZHRiUiIiItSSVwbG90R0YlNiQtRis2I0kieEdGJS9GNDtJI3gwR0YlRi0=Only re-execute the following code repeatedly, changing the value of N through the values 0,1,2,3,... (starting at any integer that seems convenient) by trial and error until you get exactly what you want. The value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGLy9GNUY5Rjc= is the number of times you halve the initial interval division of 50 to achieve this. The additional looping is for your convenience so you don't have to execute this repeatedly for each new value of the stepsize, and the loop index LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the number of times you double the number of steps to get the current number. (Note that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is the power of 2 used to increase the initial division into 50 subintervals, i.e., the number of times the division number is doubled.)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[Notice that rounding off "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjX3lGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn" we want to get 3.437 twice in a row after rounding to 3 decimal places for this example (which is the reepeated value of "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoeV9leGFjdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=" rounded to 3 decimal places), so that explains where we stopped here at 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: this is different than just getting the first 3 decimal places correct, which occurs already at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJjEyODAwRidGOUY5, when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjhGJ0Y5Rjk=.]
[Put your final comment here, like: "We had to double the number of steps 11 times to get the correct 3 decimal place answer after rounding off, twice in a row." Also put in the answer to the error halving question: roughly by what factor does the error decrease each time you half the stepsize? Look at the successive "_error" results to draw your conclusion.]
[When you are done, delete all this extra stuff in brackets, please. For your convenience, a separate file is already set up for you to only use this part of the worksheet.]LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=EulerTutorThis tutor requires the insertion of 1-d math: 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. It also does not show the calculations, only the final approximation.LSYmSShTdHVkZW50RzYiNiNJMk51bWVyaWNhbEFuYWx5c2lzR0YmNiNJK0V1bGVyVHV0b3JHRiZGJg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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