AMME2000_AMME2960_Assignment1.pdf - AMME2000\/2960 Assignment 1 Due 11:59 pm Thursday 29th March Assignment Information This assignment is split in two
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AMME2000/2960 - Assignment 1Due: 11:59 pm Thursday 29thMarchAssignment InformationThis assignment is split in two sections. You are to write a report summarising your results in aWord Document or PDF, this means no handwritten answers whatsoever. 10% of the assignmentmarks are allocated to report formatting and presentation.The report should not exceed 1000words, any additional words will not be marked. All figures and tables in the report must be num-bered and discussed.An electronic copy of the report should be submitted to Turnitinby 11:59 pm Thursday 29thMarch.Late submissions will be deducted 5% per daylate.Section 1: Taylor Series ApproximationsIn this section of the assignment you are required to compute, analyse and discuss the accuracy oftwo numerical approximations to the second derivative of the function;f(x) = tanh(x)(1)The two approximations you will consider are a 4-point and 5-point finite difference stencil:fxx(xi)≈-fi-3+ 4fi-2-4fi-1+fi+12Δx2+(2)fxx(xi)≈-fi-2+ 16fi-1-30fi+ 16fi+1-fi+212Δx2+(3)where Δxis the grid spacing,fi=f(xi) andis the truncation error. For the written report:1. Use the Taylor Series expansion to derive the leading order error for both of the stencilsprovided.Leave your final solution in terms of Δx.Make sure you take into account thecorrect sign of your answer! (15%)2. Write two Matlab functions to evaluate the two numerical stencils over the domain