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Convergence of a Numerical Technique via Interpolating Function to Approximate Physical Dynamical Systems

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In this research study, a numerical technique recently devised via interpolating function to solve initial value problems in ordinary differential equations has thoroughly been investigated for its convergence, consistency, stability and truncation error analysis. The proposed numerical technique is found to be third order convergent besides being consistent, and conditionally stable. The leading term of the local truncation errors for the proposed technique has been derived using the well-known Taylor's series expansion and Lax's equivalence theorem later proves its third order convergence. Some initial value problems of varying nature (linear, non-linear, autonomous and non-autonomous) have numerically been solved to test the performance of the technique in terms of the maximum absolute relative errors, absolute relative errors computed at the final nodal point of the associated integration interval, the l 2-error norm, and the computer time measured in seconds. All the necessary computations have been carried out via MATLAB Version: 9.2.0.538062 (R2017a) in double-precision.
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Keywords: AUTONOMOUS; CONSISTENCY; LAX'S EQUIVALENCE THEOREM; LINEAR STABILITY; LOCAL ERROR

Document Type: Research Article

Publication date: September 1, 2018

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  • Journal of Advanced Physics is an interdisciplinary peer-reviewed journal consolidating research activities in all experimental and theoretical aspects of advanced physics. The journal aims in publishing articles of novel and frontier physics that merit the attention and interest of the whole physics community. JAP publishes review articles, full research articles, short communications of important new scientific and technological findings in all latest research aspects of physics.
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