1. Use a Lagrange interpolating polynomial of the first and second order to evaluate the value...
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1. Use a Lagrange interpolating polynomial of the first and second order to evaluate the value of y at x = 25 based on the data in the following table; X 10 30 50 0.424 7.7 1.6 y a) Solve by hand by using first-order polynomial and the second-order polynomial b) Draw the flow chart expressing the algorithm for the solution. c) Create an m-script containing a function evaluating the y-values for the pre-defined x-values by means of Lagrange's Interpolation Method. i. Write the MATLAB Code (m-script) on the answer sheet. ii. Add explanation (comment) with (%) for each line of MATLAB Code. iii. Build the m-script in MATLAB. iv. Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. 1.2 2. Evaluate the integral1 e* dx, taking n = 5 using Simpson's 1/3 rule. a) Evaluate by hand using Simpson's Rule. b) Draw the flow chart expressing the algorithm for the solution. c) Create an m-script utilizing Simpson's 1/3 rule to evaluate this integral. i. Write the MATLAB Code (m-script) on the answer sheet. ii. Add explanation (comment) with (%) for each line of MATLAB Code. iii. Build the m-script in MATLAB. iv. Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. 3. For the following differential equation: dy 5e0.6t - 2y; for 0 t 3, y(0)=1.5 n=5. dt a) Solve this differential equation by using fourth-order Runge-Kutta Method. b) Draw the flow chart of the algorithm for the solution of this solution. c) Perform the following; i) Write the MATLAB Code (m-script) on the answer sheet. ii) Add explanation (comment) with (%) for each line of MATLAB Code. iii) Build the m-script in MATLAB. iv) Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. = la lb-i lb-ii lb-iii 1b-iv 2a 2b 2c-i 2c-ii 2c-iii| 2c-iv 3a 3b-i 3b-ii 10 10 10 2 1,5 1,5 5 2 10 10 10 10 5 3 3b-iii| 3b-iv 3c-i 3c-ii 3c-iii 2 2 2 2 2 1. Use a Lagrange interpolating polynomial of the first and second order to evaluate the value of y at x = 25 based on the data in the following table; X 10 30 50 0.424 7.7 1.6 y a) Solve by hand by using first-order polynomial and the second-order polynomial b) Draw the flow chart expressing the algorithm for the solution. c) Create an m-script containing a function evaluating the y-values for the pre-defined x-values by means of Lagrange's Interpolation Method. i. Write the MATLAB Code (m-script) on the answer sheet. ii. Add explanation (comment) with (%) for each line of MATLAB Code. iii. Build the m-script in MATLAB. iv. Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. 1.2 2. Evaluate the integral1 e* dx, taking n = 5 using Simpson's 1/3 rule. a) Evaluate by hand using Simpson's Rule. b) Draw the flow chart expressing the algorithm for the solution. c) Create an m-script utilizing Simpson's 1/3 rule to evaluate this integral. i. Write the MATLAB Code (m-script) on the answer sheet. ii. Add explanation (comment) with (%) for each line of MATLAB Code. iii. Build the m-script in MATLAB. iv. Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. 3. For the following differential equation: dy 5e0.6t - 2y; for 0 t 3, y(0)=1.5 n=5. dt a) Solve this differential equation by using fourth-order Runge-Kutta Method. b) Draw the flow chart of the algorithm for the solution of this solution. c) Perform the following; i) Write the MATLAB Code (m-script) on the answer sheet. ii) Add explanation (comment) with (%) for each line of MATLAB Code. iii) Build the m-script in MATLAB. iv) Run the m-script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard. = la lb-i lb-ii lb-iii 1b-iv 2a 2b 2c-i 2c-ii 2c-iii| 2c-iv 3a 3b-i 3b-ii 10 10 10 2 1,5 1,5 5 2 10 10 10 10 5 3 3b-iii| 3b-iv 3c-i 3c-ii 3c-iii 2 2 2 2 2
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1 Lagrange Interpolating Polynomial a Solving by hand using the firstorder polynomial y y0 x x1 x0 x1 y1 x x0 x1 x0 Substituting the given values x0 10 y0 77 x1 30 y1 16 and x 25 we get y 77 25 30 10 ... View the full answer
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