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Approximate and Exact Solution of Linear and Nonlinear Schrödinger Equation using Sawi Transform coupled with Homotopy Perturbation Method Olubanwo, Oludapo O.; Adepoju, Julius; Ajani, Abiodun Sufiat; Idowu, Senayon Sunday; Ifeyemi, Opeyemi
Indonesian Journal of Mathematics and Applications Vol. 2 No. 2 (2024): Indonesian Journal of Mathematics and Applications (IJMA)
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2024.002.02.1

This study presents an approximate solution using the Sawi Transform Method for the Schrödinger equation. Four problems were considered to illustrate the Sawi Transform Homotopy perturbation Method’s (STHPM) effectiveness and capabilities. The equation below is subjected to the Sawi Transform combined with Homotopy Perturbation Method (STHPM). $i\frac{\partial}{\partial t}\\psi(z,t)+\Delta[\psi(z,t)]+N\psi(z,t)=0$ The results obtained are represented in a series of rapidly convergent terms.

Approximate and Exact Solution of Linear and Nonlinear Schrödinger Equation using Sawi Transform coupled with Homotopy Perturbation Method Olubanwo, Oludapo O.; Adepoju, Julius; Ajani, Abiodun Sufiat; Idowu, Senayon Sunday; Ifeyemi, Opeyemi
Indonesian Journal of Mathematics and Applications Vol. 2 No. 2 (2024): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2024.002.02.1

This study presents an approximate solution using the Sawi Transform Method for the Schrödinger equation. Four problems were considered to illustrate the Sawi Transform Homotopy perturbation Method’s (STHPM) effectiveness and capabilities. The equation below is subjected to the Sawi Transform combined with Homotopy Perturbation Method (STHPM). $i\frac{\partial}{\partial t}\\psi(z,t)+\Delta[\psi(z,t)]+N\psi(z,t)=0$ The results obtained are represented in a series of rapidly convergent terms.

Topological Existence and Uniqueness of the Mahgoub–Adomian Decomposition Method Adepoju, Julius; Ajani, Abiodun Sufiat; Olubanwo, Oludapo Omotola; Onitilo, Sefiu Adekunle; Oduyemi, Oluwadamilare Segun
Indonesian Journal of Mathematics and Applications Vol. 4 No. 1 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.01.1

We develop a rigorous topological theory for the Mahgoub--Adomian Decomposition Method (MADM) in the setting of Banach spaces. The method is formulated as a nonlinear operator equation in the space $C([0,T];H^s(\Omega))$, where the associated Mahgoub--Adomian operator is shown to be continuous and compact. Existence of the MADM solution is established via Schauder’s fixed-point theorem, while uniqueness follows under a strict monotonicity condition on the nonlinear operator. The analysis is carried out independently of contraction assumptions or smallness conditions. The results are applied to both linear and nonlinear Schrödinger equations of the form $i u_t + \Delta u + N(u) = f(x,t), \quad u(x,0)=h(x)$, including the linear problems $N(u)=0$ and nonlinear problems such as $N(u)=\lambda |u|^{p}u$. These results provide a topological well-posedness framework that justifies the convergence and uniqueness of the Mahgoub--Adomian decomposition series for a broad class of Schrödinger-type evolution equations.

Existence, Uniqueness, and Convergence of the Coupled Mahgoub-Adomian Decomposition Method for Volterra-Fredholm Integro-Differential Equations Bello, Kareem; Adepoju, Julius; Onitilo, Sefiu A.; Ogundele
Indonesian Journal of Mathematics and Applications Vol. 4 No. 2 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.02.2

The current paper presents a detailed study of the application of the Coupled Mahgoub-Adomian Decomposition Method (CMADM) to solve both linear and nonlinear Volterra and Fredholm IDEs. The current method includes the effectiveness of the application of the Mahgoub integral transform along with the efficiency of the use of the ADM to handle the nonlinearity in the problem. In addition, existence and uniqueness theorems for the solutions of IDEs via the Banach fixed point theorem and the Picard iteration process are proved for the first time. Convergence of the generated series via the current method is investigated via the Cauchy-estimate bound on the Adomian polynomials, which replaces the unjustified linear estimate used in a previous version of this paper, and norm estimates in a suitable Banach space. Conditions under which the accuracy of the result after truncation of the series can be achieved are derived. We specify what is new in comparison with the existing Laplace, Sumudu, and Elzaki Adomian methods; we fix two inaccuracies found in the referee review process: an erroneous “exact solution” of one nonlinear problem, and an arithmetic mistake in the Fredholm example; and we add one more nonlinear problem with an oscillatory kernel along with convergence rate tables and error graphs. As an illustration, four examples, including one linear and three nonlinear integro-differential equations, are considered.

A Delay Differential Equation Model for Nipah Virus Transmission with Vaccination and Hospital Amplification Onitilo, Sefiu; Adepoju, Julius; Ajani, Abiodun S.; Haruna, Hammed A.; Ayeni, Sheriffat T.; Odetunde, Opeyemi
Indonesian Journal of Mathematics and Applications Vol. 4 No. 2 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.02.5

Nipah virus (NiV) is a deadly zoonosis capable of human-to-human transmission and amplification via hospital settings. In this paper, we formulate a delay differential equations model of NiV with seven states (susceptible, vaccinated, exposed, asymptomatically infected, symptomatically infected, hospitalized, and recovered) considering incubation delay, partial vaccine efficacy, waning immunity, and transmission within hospitals. The basic reproduction number R₀ is calculated using the next-generation matrix approach. If R₀ < 1, then there is global stability of the disease-free equilibrium; and an endemic equilibrium exists uniquely when R₀ > 1. Simulations using parameter values based on outbreaks in Bangladesh and Malaysia reveal that human-to-human transmission outdoes zoonotic spillover, while vaccination rate and efficacy and recovery rate in hospitals emerge as key control parameters.

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