In Problems 1 through 8, compute the successive approximation formula to compute
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- Using MATLAB, develop a computer program for the finite difference solution with general θ scheme for the 1D consolidation of a uniform layer of soil. Compare the results for θ=0, 0.5, 2/3 and 1.0 for α=0.49 and α=0.51 against the analytical solution of Terzaghi’s equation for T=0.5. Apply the program to both cases of double draining layer and single draining layer.arrow_forwardA circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forwardThe results of an experimental study (x variable, y function) are given in the table below. (Five digits will be taken after the comma.) a-Find First, Second, and Third Order Linear Interpolation Polynomials. b- Find y(2)=? for First, Second, and Third Order Linear Interpolation Polynomials i 1 3 3 4 2,5 6,5 7arrow_forward
- please explain each steparrow_forwardFirst Solve with: X = 5Secondly Solve with: X = 2arrow_forwardYou work as a software engineer in a company that develops software for providing approximate numerical solutions to complex mathematical problems. Your manager asked you to develop two software products for (i) finding the roots of complex functions and (ii) performing complex integrations. Task 4: i) Compute the integral of f(x)= 3x from a = 0 to b = 9 with 3 sub-intervals using the following integral approximation methods: (i) Simpson, and (ii) Mid-ordinate rules. %3Darrow_forward
- Solve by hand function bellow using Euler method. Repeat 5 times. (5 iterations) f (x) = x°-7.x+4arrow_forwardA discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4arrow_forwardA motorist found that the efficiency of her engine could be increased by adding lubricatingoil to fuel. She experimented with different amounts of lubricating oil and the data areAmount of lubricating oil (ml) 0 25 50 75 100 Efficiency (%) 60 70 75 81 84(a) (10 points) Obtain the least squares fit of a straight line to the amount of lubricatingoil.(b) (10 points) Test whether or not the slope β1 = 0. Take α = 0.05 as your level ofsignificance.(c) (10 points) Construct a 90% confidence interval on the mean response at x0 = 10 ml.(d) (10 points) Give a point estimate of the mean engine efficiency when the amount oflubricating oil is 450 ml.(e) (10 points) What additional danger is there when using your estimate in part (d)?arrow_forward
- Computer Science f(x)= Sin(x) – x 3 + C Where C = Max [0.15, (69/100)] x20, (x is in radian). Apply the false position method three iterations to find the root of the function (Decide the starting values of Xl and Xu yourself)arrow_forwardSolve the following problems using function codes in Matlab onlyarrow_forward(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr