Numerical Solutions for Third Order Ordinary Differential Equation by Differential Transform Method &amp; Elzaki Transform Method

Differential equations are commonly used to model several engineering, science, and biological applications. Unfortunately, finding analytical solutions for solving higher-order Ordinary Differential Equations (ODEs) is a challenge. Numerical methods represent a leading candidate for solving such ODEs. This work presents an innovated adaptive technique that uses polynomials to solve linear or nonlinear third-order ODEs. The proposed technique adapts the coefficients of the polynomial to obtain an explicit analytical solution. A signed least mean square algorithm is exploited to enhance the adaptation process and to decrease both computational requirements and time. The efficiency of the proposed Adaptive Polynomial Method (APM) is illustrated through six well-known examples. The proposed technique is compared with recent analytical and numerical methods to validate its effectiveness in terms of Mean Square Error (MSE) and computation time. An application in a thin film flow system is modeled to a third-order ODE. The proposed technique is compared with recent numerical and analytical methods in solving the thin film flow equation, and the proposed technique has achieved better results. Furthermore, the proposed technique provides an analytical solution with an increased dynamic range and much lower computational time than those of the conventional numerical methods.

show abstract

Adaptive Polynomial Method for Solving Third-Order ODE With Application in Thin Film Flow

Haweel

Zahran

El‐Samie

2021

IEEE Access

View full text Add to dashboard Cite

show abstract

Application of Elzaki Transform Method for Solving and Interpreting HIV Superinfection Model

Ogunniran

Ibrahim

2023

International Journal of Applied Mathematics and Informatics

View full text Add to dashboard Cite

In this work, a superinfection model of two HIV strains was proposed. The proposed model was solved and interpreted using the Elzaki Transform Method (ETM). The proposed model presented some non-linear terms which are difficult to resolve using the ETM. Hence, we employed the Adomian Decomposition Method (ADM) to resolve the nonlinear terms. We derived an iterative scheme that was used to predict the behavior of the model. Results of data simulation showed that the population of healthy CD4+ T cells declined with respect to time in the presence of HIV strains. The viral loads for both viral strains are observed to be on a steady increase. The study reveals that ETM can be used to solve Superinfection models of HIV. The method is easier, more efficient, and more effective, and it converges faster to the solution when compared to other transform methods. We recommend that ETM can be applied to superinfection and co-infection models of other infectious diseases.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Numerical Solutions for Third Order Ordinary Differential Equation by Differential Transform Method & Elzaki Transform Method

Cited by 2 publications

References 11 publications

Adaptive Polynomial Method for Solving Third-Order ODE With Application in Thin Film Flow

Adaptive Polynomial Method for Solving Third-Order ODE With Application in Thin Film Flow

Application of Elzaki Transform Method for Solving and Interpreting HIV Superinfection Model

Contact Info

Product

Resources

About