Compute tables for the Euler Method and Modified Euler Method by hand, for the IMx,(o) 1. To make these a reasonable length, you are going to find values of x(1) instead of x(2) (as in the Examples). The exact solution is xtt)2e-, which gives x(1) 0.735759 For the NP x'= t-x, x(0)-1, do the following. (Round your answers to six decimal places.) (a) Do 4 steps of the Modified Fuler Method, with At 0.25, to find an approximation to x(1). (1) 05 Do 8 steps of the Modified Euler Method, with Î x(1)-6687128 0.125, to find an approximation to x(1). (b) Complete the following table (values are from Example 2.6.2). error in x(1) .045491 at 0.5 0.25 0.125 0.781250 (c) Are the errors in x(1) what you would expect from a second-order method? Explain. This s x what you should expect with a second-order method. The errors are multiplied by approximately 14as At is multiplied by Vieming Saved ok Revent st Responne
Show transcribed image text Compute tables for the Euler Method and Modified Euler Method by hand, for the IMx,(o) 1. To make these a reasonable length, you are going to find values of x(1) instead of x(2) (as in the Examples). The exact solution is xtt)2e-, which gives x(1) 0.735759 For the NP x'= t-x, x(0)-1, do the following. (Round your answers to six decimal places.) (a) Do 4 steps of the Modified Fuler Method, with At 0.25, to find an approximation to x(1). (1) 05 Do 8 steps of the Modified Euler Method, with Î x(1)-6687128 0.125, to find an approximation to x(1). (b) Complete the following table (values are from Example 2.6.2). error in x(1) .045491 at 0.5 0.25 0.125 0.781250 (c) Are the errors in x(1) what you would expect from a second-order method? Explain. This s x what you should expect with a second-order method. The errors are multiplied by approximately 14as At is multiplied by Vieming Saved ok Revent st Responne