An Orthogonal-Based Block Hybrid Method for the Solution of Third Order Ordinary Differential Equations

An orthogonal polynomial of the weight function w(x) = x 2+x+1 in the interval [-1, 1] was created as the basis function in block methods using the collocation and interpolation methodology. For third-order problems, an efficient class of continuous and discrete numerical integration techniques of implicit hybrid form were devised and effectively implemented. These schemes were used to address three separate problems and their performances evaluated. Using the existing theorems to investigate our new methods, the inquiry proves that the methods are consistent, zero-stable, and are therefore convergent.