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# Diff Equ & Lin Algebra MATH 2250

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This 4 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 2250 at University of Utah taught by Grant Gustafson in Fall. Since its upload, it has received 17 views. For similar materials see /class/229923/math-2250-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

Math 2250 Report Contents 242526 Problem 12 September 2004 Exact Solution 24252612 The exact solution should be derived by hand just once for 2 412 and then only referenced in 2 512 2 612 do not derive again The answer I 7 4 z 7 2 y A table of exact values is required in order to make comparison tablesi Make this table for each problem separately as the values used vary from one comparison to another 24 Notes Numerical Solution 2412 This work has to be done before you can write the report Please write a report that references an appendix to be attached as a worksheet print see below for the content of the appendix lnclude here handwritten material that describes the Euler algorithm as applied to problem 12 then reference the worksheet for results The maple code referenced in the lQpage internet document Numerical DE Manuscript will be used There is a text le of the actual code segments in the internet document document Numerical DE maple coding hintsi Both at the course web site To start get the sample code to produce correct answers to the example supplied in the text le sourcei Once correct modify the code for 12 The step size h 0 01 produces a dot table of 101 rows whereas the step size h 0005 makes a dot table with 201 rows There is no reason to include all of this data in an appendix see notes belowi The term percentage error is de ned by lapproz 7 ezactl Error 100 lezactl This equality is also called the percentage relative error Comparison Table 2412 Most of the h 0 01 and h 0005 data is not used in the report You must select the data to be printed in the table from the raw data produced in Maple Loop control should be used to create the dots table but the dots table should not be printed in its entirety in the nal report Please do not print data that is not used as it makes the reports too long and it wastes paperi Observe that the percentage error can be computed from the 6item table nd just the error values for z 00i20i40i60i8 10 The comparison will be 6 rows in 2 512i The table should list I yl y2 y El E2 where yl is the h 0 01 approximate value y is the h 0 005 approximate value y is the exact value El is the percentage error for h 0 01 and E2 is the percentage error for h 0005 The zvalues in the table are 00 0 2 0 4 0 6 0 8 10 Graphics 2412 There should be three graphics one for h 001 one for h 0005 and one for the exact solution All are produced in maplei Reference the maple worksheet appendixi Appendix Hand Solution Steps 2412 lnclude a derivation of the numerical values for line two of the dots table for each case h 0 01 and h 0005 Show all steps by hand This is the only crosscheck on the numericsi Appendix Maple Worksheet 2412 Attach a print of the maple worksheet that contains all computer code and data used in 2412i Reference this appendix during the report 25 Notes Numerical Solution 2512 This work has to be done before you can write the report Please write a report that references an appendix to be attached as a worksheet print see below for the content of the appendix lnclude here handwritten material that describes the Heun modi ed Euler algorithm as applied to problem 12 then reference the worksheet for results To start get the sample Heun code to produce correct answers to the example supplied in the text le source Once correct modify the code to apply to 2512i The step size h 001 produces a dot table of 101 rows Comparison Table 2512 The comparison will be 6 rows in 2512i The table should list I y1 y2 y E1 E2 where y1 is the h 001 approximate value y2 is the h 0005 approximate value y is the exact value E1 is the percentage error for h 001 and E2 is the percentage error for h 0005 The zvalues in the table are 00 02 04 06 08 10 Graphics 2512 There should be three graphics one for h 001 one for h 0005 and one for the exact solution All are produced in maple Reference the maple worksheet appendix Appendix Hand Solution Steps 2512 Include a derivation of the numerical values for line two of the dots table for h 001 Show all steps by hand Don7t show any h 0005 steps This is the only crosscheck on the numerics Appendix Maple Worksheet 2512 Attach a print of the maple worksheet that contains all computer code and data used in 2512i Reference this appendix during the production of the report 26 Notes Numerical Solution 2612 This work has to be done before you can write the report Please write a report that references an appendix to be attached as a worksheet print see below for the content of the appendix lnclude here handwritten material that describes the RK4 algorithm as applied to problem 12 then reference the worksheet for results To start get the sample RK4 maple code referenced in the 19page internet document Numerical DE Manuscn39pt to produce correct answers to the example supplied in the text le source Once correct modify the code for 12 The step size h 02 produces a dot table of 6 rows For h 01 there are 11 rows Comparison Table 2612 The comparison will be 6 rows in 2612i The table should list I y1 y2 y E1 E2 where y1 is the h 02 approximate value y2 is the h 01 approximate value y is the exact value E1 is the percentage error for h 02 and E2 is the percentage error for h 01 The zvalues in the table are 00 02 04 06 08 10 Graphics 2612 There should be three graphics7 one for h 027 one for h 0 1 and one for the exact solution All are produced in maplel Reference the maple worksheet appendixl Appendix Hand Solution Steps 2612 Skip this step for 26127 because the machine is likely more reliable than a hand calculationi Instead of a hand check7 check the algorithm on several problems which have known solutionsi Appendix Maple Worksheet 2612 Attach a print of the maple worksheet that contains all computer code and data used in 2 612l Reference this appendix during the production of the report Math 2250 Problems 14 Redo Notes September 2003 Problem 14 1l Find the general solution for y 21y 0 Find the equilibrium implicit and explicit solutions The equilibrium solution is y 0 In one detail 61quot m reduces to m which is written as iyl The nonequilibrium solution is y yoe le Explain why the two solutions collapse into the books answerl Problem 14 5l Find the general solution for Q y 1 7 y Find the equilibrium implicit and explicit solutions The equilibrium solutions are y l and y 71 The implicit solution is sin 1 y cl An explicit solution y sink5 c is valid for domain D z 2 0 cosE c 2 0 Reports should contain four 4 solution checks The books answer is incorrect Problem 14 11l Find the general solution for y zygl Find the equilibrium implicit and explicit solutions The equilibrium solution is y 0 The implicit solution is y 2 c 7 12 Explicit solutions are y i Gigs valid for domain D z z c 7 12 gt 0 Reports should contain two 2 solution checks The books answer is correct for the nonequilibrium solution provided you supply the missing it

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