Pub Date : 2025-10-23DOI: 10.1007/s11144-025-03004-w
Manzoor Hussain, Abdul Ghafoor
We present a meshless method of lines for efficiently simulating two-dimensional nonlinear reaction–diffusion systems. Using positive-definite radial kernels, we derive approximate particular solutions via the Laplace operator and superimpose them to approximate unknown fields and their spatial derivatives without mesh generation. The resulting ordinary differential system is integrated with a high-order solver. We theoretically establish and numerically verify the method’s stability and positivity-preserving properties, ensuring dynamical consistency with the underlying PDEs. Benchmark tests on cross-diffusion Brusselator systems confirm accuracy, robustness, and geometric flexibility. Compared with leading mesh-based and meshless schemes, our approach offers a compatible and high-order framework for reaction–diffusion problems on complex domains.
{"title":"Meshless method of approximate particular solution for a two-dimensional cross-diffusion brusselator system","authors":"Manzoor Hussain, Abdul Ghafoor","doi":"10.1007/s11144-025-03004-w","DOIUrl":"10.1007/s11144-025-03004-w","url":null,"abstract":"<div><p>We present a meshless method of lines for efficiently simulating two-dimensional nonlinear reaction–diffusion systems. Using positive-definite radial kernels, we derive approximate particular solutions via the Laplace operator and superimpose them to approximate unknown fields and their spatial derivatives without mesh generation. The resulting ordinary differential system is integrated with a high-order solver. We theoretically establish and numerically verify the method’s stability and positivity-preserving properties, ensuring dynamical consistency with the underlying PDEs. Benchmark tests on cross-diffusion Brusselator systems confirm accuracy, robustness, and geometric flexibility. Compared with leading mesh-based and meshless schemes, our approach offers a compatible and high-order framework for reaction–diffusion problems on complex domains.</p></div>","PeriodicalId":750,"journal":{"name":"Reaction Kinetics, Mechanisms and Catalysis","volume":"139 1","pages":"47 - 70"},"PeriodicalIF":1.7,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1007/s11144-025-02992-z
Soheila Zandi Lak, Mohammad Reza Rahimpour, Maryam Meshksar
In this work, hollow ZnO spheres (HS–ZnO) were synthesized via a glucose-templated hydrothermal route, and their structural, textural, and photocatalytic properties were systematically optimized. The HS–ZnO exhibited a large surface area (96.35 m2g−1), uniform hollow morphology, and a narrower band gap (3.12 eV) compared with commercial ZnO. These features enhanced light absorption, charge separation, and adsorption capacity. Under optimized conditions (5 g L−1 catalyst, pH 5,120 min UV irradiation, and 5 mg L−1 Ni(II)), HS–ZnO achieved 88.16% Ni(II) removal, more than twice the efficiency of commercial ZnO (41.37%). Kinetic studies confirmed a pseudo-second-order model, while adsorption equilibrium followed the Freundlich isotherm, indicating chemisorption on heterogeneous surfaces. Control experiments revealed that photoreduction was the dominant pathway. HS–ZnO maintained 76.2% efficiency after five cycles, demonstrating excellent stability and reusability. These results establish morphology-controlled HS–ZnO as a cost-effective and robust photocatalyst for Ni(II) removal from aqueous solutions.