Order Six Block Integrator for the Solution of First-Order Ordinary Differential Equations

Abstract

In this research work, we present the derivation and implementation of an order six block integrator for the solution of first-order ordinary differential equations using interpolation and collocation procedures. The approximate solution used in this work is a combination of power series and exponential function. We further investigate the properties of the block integrator and found it to be zero-stable, consistent and convergent. The block integrator is further tested on some real-life numerical problems and found to be computationally reliable.

Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

“…Showing results for decay model problem. 1-3 because the iteration per step in the new method was lower than the method proposed by [17]. Our method was found to be zero stable, consistent and converges.…”

“…Problems 1 and 2 and 3 were solved by Sunday et al [17]. They proposed an order six block integrator for the solution of first-order ordinary differential equations.…”

“…Applying our new half step numerical scheme (8) to solve SIR model simplified as (17) gives results as shown in Table 1.…”

“…Note that, which is also the expression for the mass of the substance at any time t. Applying our new half step numerical scheme (8) to solve the Growth model (22) gives results as shown in Table 3 [16,17] (Table 3). …”

“…We also assume that   N t is the population size at time ( Table 2). t The theoretical solution of (18) Applying our new half step numerical scheme (8) to solve the Growth model (17) gives results as shown in Table 2 [16].…”