Journal of the Nigerian Mathematical Society

Block Bi-Basis Collocation Method for Direct Approximation of Fourth-order IVP

Blessing Iziegbe Akinnukawe — 2023-04-24

This study presents the derivation of two-step fifth-order hybrid scheme based on the combination of Hermite and shifted Chebyshev polynomials as bases functions of the collocation techniques. The technique was used to generate a set of hybrid schemes at selected grid and non-grid points and implemented as a block method. The derived block method (Block Bi-basis Collocation Method) was applied as a simultaneous integrator to linear and non-linear fourth-order initial value problems of ordinary differential equations. The zero stability, order, error constants, consistency, convergence and numerical results of the proposed block method are analysed. The application of the block bi-basis collocation method to some fourth-order initial value problems demonstrated the effectiveness and accuracy of the method. The block bi-basis collocation method compared favorably with existing methods in literature.

Hyers-Ulam Stability Theorems for Second Order Nonlinear Damped Differential Equations with Forcing Term

Ilesanmi Fakunle — 2023-04-24

In this paper Hyers-Ulam stability theorems of nonlinear second order damped differential equations with forcing are considered. By using the Bihari inequality and Gronwal-Bellman-Bihari integral inequality, we obtain new suffient conditions for the Hyers-Ulam stability of every nonlinear second order differential equation considered. Our results improve and extent some known results.

Further results on stability criteria for certain second-order delay differential equations with mixed coefficients

Omeike Mathew Omonigho — 2023-04-24

This work investigates the asymptotic stability of the trivial solution of the second-order linear delay differential equation
$$y''(t)=p_1y'(t)+p_2y'(t-\tau)+q_1y(t)+q_2y(t-\tau),$$ where $\tau>0,p_1,p_2,q_1,q_2$ are real numbers. By reducing the equation to a linear second-order ordinary differential equation with constant coefficients, sufficient conditions which guarantee the asymptotic stability of the trivial solution are obtained in a very simple form.

On the Stability and Boundedness of Solutions of Certain Kind of Second Order Delay Differential Equations

Daniel Adams — 2023-04-24

In this paper, we study the second order non-autonomous nonlinear delay differential equation
$$x^{\prime\prime} + b(t)g(x,x^\prime) + c(t)h(x(t-r))m(x^\prime) = p(t,x,x^\prime)$$
for asymptotic stability of solutions when $p(t,x,x^\prime) = 0$ and the boundedness of solutions when $p(t,x,x^\prime) \neq 0.$ This work improved on some earlier results in the literature.