Journal of the Nigerian Mathematical Society <p>Journal of the Nigerian Mathematical Society (JNMS)</p> <p>JNMS provides a means of communication and exchange of ideas among workers in mathematical sciences (mathematics, mathematical physics, statistics, computer science), and offers an effective method of bringing new results quickly to the public. By doing so the journal establishes an informal vehicle enabling the field of mathematical sciences to be understood in a broad sense. It will include theoretical and experimental results, and fundamental and practical research.<br /><br /></p> Nigerian Mathematical Society en-US Journal of the Nigerian Mathematical Society 0189-8965 Block Bi-Basis Collocation Method for Direct Approximation of Fourth-order IVP <p>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.</p> Blessing Iziegbe Akinnukawe Mathew Remilekun Odekunle Copyright (c) 2022 2023-04-24 2023-04-24 42 1 1 18 Hyers-Ulam Stability Theorems for Second Order Nonlinear Damped Differential Equations with Forcing Term <p>In this paper Hyers-Ulam stability theorems of nonlinear second&nbsp; order&nbsp; &nbsp;damped differential equations&nbsp; with&nbsp; forcing&nbsp; are considered. By using the Bihari&nbsp; 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&nbsp; and extent&nbsp; some known results.</p> Ilesanmi Fakunle Peter Olutola Arawomo Copyright (c) 2023 2023-04-24 2023-04-24 42 1 19 35 Further results on stability criteria for certain second-order delay differential equations with mixed coefficients <p>This work investigates the asymptotic stability of the trivial solution of the second-order linear delay differential equation <br>$$y''(t)=p_1y'(t)+p_2y'(t-\tau)+q_1y(t)+q_2y(t-\tau),$$ where $\tau&gt;0,p_1,p_2,q_1,q_2$ 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.</p> Omeike Mathew Omonigho Copyright (c) 2023 2023-04-24 2023-04-24 42 1 36 48 On the Stability and Boundedness of Solutions of Certain Kind of Second Order Delay Differential Equations <p>In this paper, we study the second order non-autonomous nonlinear delay differential equation <br>$$x^{\prime\prime} + b(t)g(x,x^\prime) + c(t)h(x(t-r))m(x^\prime) = p(t,x,x^\prime)$$<br>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.</p> Daniel Adams Mathew Omeike Idowu Osinuga Biodun Badmus Copyright (c) 2023 2023-04-24 2023-04-24 42 1 49 59