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Ajani, Abiodun Sufiat
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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

Abstract

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

Abstract

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

Abstract

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.
Co-Authors Adepoju, Julius Idowu, Senayon Sunday Ifeyemi, Opeyemi Oduyemi, Oluwadamilare Segun Olubanwo, Oludapo O. Olubanwo, Oludapo Omotola Onitilo, Sefiu Adekunle