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1 – 3 of 3Azzh Saad Alshehry, Humaira Yasmin, Rasool Shah, Amjid Ali and Imran Khan
The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation…
Abstract
Purpose
The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.
Design/methodology/approach
In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.
Findings
We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.
Originality/value
Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.
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Keywords
Yarong Zhang and Meng Hu
The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering…
Abstract
Purpose
The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.
Design/methodology/approach
This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.
Findings
Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.
Originality/value
The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.
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Keywords
Nisha, Neha Puri, Namita Rajput and Harjit Singh
The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing…
Abstract
Purpose
The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.
Design/methodology/approach
In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.
Findings
As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.
Research limitations/implications
Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.
Practical implications
This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.
Social implications
The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.
Originality/value
It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.
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