A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions

One of the well-known schemes for direct numerical integration second-order initial-value problems is due to Falkner. This paper focuses on construction a family adapted block Falkner methods which are frequency dependent solution initial value with oscillatory solutions. The techniques collocation and interpolation adopted here derive new methods. study properties proposed reveals that they consistent zero-stable, thus, convergent. Furthermore, stability analysis algebraic order conditions established. As may be seen from results, resulting efficient competitive compared some recent in literature.