Abstract

COMPREHENSIVE ANALYSIS OF 3-QUARTER-STEP COLLOCATION METHOD FOR DIRECT INTEGRATION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS USING TAYLOR SERIES FUNCTION

aAdoghe L. O., bOmole E. O,

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Abstract In this paper, we studied the numerical solutions of second order ordinary differential equation initial value problems. A continuous fractional implicit Three-Quarter methods capable of solving initial value problems of general and special second order ordinary differential equations was developed using the collocation and interpolation technique. Taylor series expansion of exponential function is used to provide an approximate solution. The method developed has the advantage of easy change of step length and evaluation of functions at off-step points. The Block method used to implement the main method guarantees that each discrete method obtained from the simultaneous solution of the block has the same order of accuracy as the main method. The new methods are zero-stable, convergent and gives high order of accuracy with very low error constants, and small intervals of absolute stability. Some examples of linear, nonlinear and stiff problems have been used to test the performance of the methods. Computed results and the associated errors were compared with the exact solutions and errors of results obtained from existing methods, respectively. The results show that the new method is efficient and more accurate than other recent methods in the literature. Keywords: Taylor Series, 3-quarter-Step, collocation method, Second order, 0-stability

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