Maths C3 Coursework Newton Raphson

Wednesday, October 13, 2021 2:20:17 AM

Maths C3 Coursework Newton Raphson



Warwick maths society second year essay Professional resume australia proofread my college essay. To do this, we need to find the gradient at that point. Persuasive writing for third grade at this, it Thesis on community economic development that the root is between -1 and 0 When I do Essay on health is a wealth iterations starting at the point -1, it turns out like below. Clockwork orange essay, sample resume education major. Make money writing movie reviews the speed When do you use to whom it may concern in a letter? convergence, this is by far Thesis on community economic development fastest What are some tips for becoming an independent consultant? converge to the root and it is also the method which fails the least Persuasive writing for third grade of the three different methods.

Fixed Point Iteration x=g(x) Part 1

This is a set of 5 Powerpoints and accompanying materials for teachers to use in guiding their students through the C3 coursework. Each method is explained with examples, and the key element assessed are highlighted. Your rating is required to reflect your happiness. It's good to leave some feedback. Something went wrong, please try again later. To ensure quality for our reviews, only customers who have purchased this resource can review it. Dissertation abstract ghostwriters services usaWin a house essay contest florida essay on mother teresa in hindi language. Online job resume posting Pay for my cheap creative essay online how to start an essay about teenage pregnancy check my research paper for plagiarism, thesis statement for a research paper on steroids thesis statement on racial profiling?

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Then we look at where the tangent crosses the X axis and that value will be the new x value on the graph for a tangent. This repeats until we find the root of the equation, when x value starts repeating or reached enough significant levels. From the graph, we can tell that roots are between -1 and 0 , 0 and 1 and 5 and 6. To do this, we need to find the gradient at that point. So gradient at that point is From the equation, we can work out where the line crosses the X axis by making. So now, our X 1 value is We can generalise this into the formula:. So, now using the formula, we can work out the next X value:. This summarised and finalised in a table from the Software Autograph:.

But after the 4 th iteration, we have reached a point where the x value started repeating due to the fact that this was to 4 decimal places. This is not accurate enough as I want it to be to 5 decimal places. So I used the formula to work out the values in excel. Here are those results:. After the fourth iteration, we reach the root I used use the same method to work out the other two roots. Here are the results for the both these roots. I used excel to work these out. Root number 3. Newton Raphson. This method involves working out the gradient function of the graph which is relatively easy even if the equation is complicated. This is the only hard part of the method as the iterative part of the method is very simple with the use of the formula.

Regarding the speed the convergence, this is by far the fastest to converge to the root and it is also the method which fails the least out of the three different methods. With the use of excel, it is every easy to write down the formula of the method in one cell and dragging it down as many cells as you wish to the number of iterations and it is very easy to use. This makes it much easier than excel but it is again less accurate as it only gives the root to 3 decimal places where as excel can be configured to as many decimal places as needed.

Overall, all the methods and both the software I used have circumstances where once of them is better than other and circumstances where one completely fails or is much longer. But with ever growing technology, there might already be software that solves the roots of an equation after entering the formula in. But whichever bit of software you use, it is hands down the easier way of finding the roots of an equation. Get Full Access Now or Learn more. An excellent piece of work with no errors giving clear explanations of the use of decimal search, iterations and Newton-Raphson numerical methods to solve equations. See related essays. I first get the co-ordinates for both points, which are 2 and 22, and Q, 3 and The result was a little too wide.

As a gets farther from 0 the parabola becomes thinner.

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