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Title: On the accuracy of the backward difference formula of order four and runge-kutta of order four in solving a first order non-linear ordinary differential equation
Authors: Nweke, Ijeoma Anie
Keywords: Accuracy
Differential equation
Issue Date: Jul-2016
Publisher: Kampala International University, School of Engineering and Applied Sciences
Abstract: In this study, the researcher investigated if the Runge-Kutta of order 4 method (RK4) is as accurate as the Backward Difference Formula of order 4 (BDF4) in solving a 1st order non-linear Ordinary Differential Equation? Two 1st order non-linear ODE were tested to analyse this problem. The RK4 proved to be more accurate than the BDF4 because the RK4 can generate it’s values without depending on the Analytic method and it showed very slight deviation from the Analytic method when it was rounded off to 9 decimal places, otherwise it was equal to the Analytic method when rounded off to 7 decimal places in equation 1 and 6 decimal places in equation 2. It shows very slight deviation from the Analytic method while the BDF4, despite it’s using starting values from the Analytic method showed large deviation from the Analytic method even when applied to the two tested problems. Even then, BDF4 is more prefered than the RK4 in solving stiff problems because it is A-Stable and converges easily.
Description: A thesis presented to the college of higher degrees and research Kampala International University Kampala, Uganda in partial fulfillment of the requirements for the Degree of Master of Science in Applied Mathematics (MSC-AM)
Appears in Collections:Master of Science in Applied Mathematics

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