The Construction of Implicit One-step Block Hybrid Methods with Multiple Off-grid Points for the Solution of Stiff Differential Equations

This paper is focused on the construction and implementation of implicit one-step hybrid block methods for the solution of stiff ordinary differential equation. The research further investigates the basic properties of implicit one-step block hybrid method. We noticed that the moment the value of an error constant is positive, the order P is odd. And when the value of an error constant is negative then the order P is of even number and the block hybrid method with three off-grid point is of uniform order. The performance of the methods was demonstrated on some stiff initial value problems (IVPs). The result revealed that the hybrid block methods are efficient, accurate and convergent on some stiff ordinary differential equations.