CHEBYSHEV HYBRID MULTISTEP METHOD FOR DIRECTLY SOLVING SECOND-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS
A numerical method had been proposed in this work for directly solving second-order initial and boundary value problems in ordinary differential equations. The approach of collocation of a derivative function at equidistant grid and offgrid points x = xn+i/3, i = 0, 1, · · · , k, where k is the step number in the interval [xn, xn+k] was adopted. The derived Chebyshev Hybrid Multistep Method (CHMM) is of order (2k + 3). The continuous scheme was evaluated at different off-step points to obtain multiple hybrid schemes of uniform order which were solved simultaneously for dense approximations that make its computation competitive. Some numerical examples were given to demonstrate the accuracy and efficiency advantages of the proposed method.
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