Numerical solution and mathematical modelling of mass transport from medicated stent

In this study, we look at the solutions of nonlinear partial differential equations and ordinary differential equations. Scientists and engineers have had a hard time coming up with a way to solve nonlinear differential equations. Almost all of the nature’s puzzles have equations that aren’t linear. There aren’t any well-known ways to solve nonlinear equations, and people have tried to improve methods for a certain type of problems. This doesn’t mean, however, that all nonlinear equations can be solved. With this in mind, we’ll look at how well the variation approach works for solving nonlinear DEs. Different problems can be solved well by using different methods. We agree that a nonlinear problem might have more than one answer. Factorization, homotropy analysis, homotropy perturbation, tangent hyperbolic function and trial function are all examples of ways to do this. On the other hand, some of these strategies don’t cover all of the nonlinear problem-solving methods. In this paper, a new method called the variation iterative method with Laplace transformation is used to find a solution to the highly nonlinear evolution of a simple pendulum whose rotation revolves around its fixed position. When the Laplace operator is used to change the Maximum Minimum Approach, Amplitude Frequency Formulation and Variation Iteration Method (VIM) nonlinear oscillators, the results of the analysis are all the same. The method for solving nonlinear oscillators, as well as their time and boundary conditions, can be shown to be correct by comparing analytical results of VIM obtained through the Laplace transformation.

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Mathematical modeling and simulation of biophysics systems using neural network

Rahman

Makhdoom

Ali

et al. 2023

Int. J. Mod. Phys. B

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Many of the real-life problems including dynamical structures can be modeled in the shape of differential equations. A number of analytic and numerical methods are being proposed for the solution of these differential equations but for some instances, we may come across a few limitations attached to them. However, theoretically strong and computationally favorable tools such as artificial neural networks can be utilized to approximate the solutions of these differential equations. In this work, we developed mathematical models for some biophysics systems on the basis of their dynamical behavior and opted a neural network having single hidden layer of 50 neurons and Broyden–Fletcher–Goldfarb–Shanno algorithm as an optimizer to simulate the results for population of micro-organisms. The graphical representations of the results obtained both from the neural network and analytic methods are compared for different parameters and we got almost the same results.

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Numerical solution and mathematical modelling of mass transport from medicated stent

Cited by 4 publications

References 39 publications

In silico drug delivery modeling of a novel Everolimus Coated Balloon

In silico drug delivery modeling of a novel Everolimus Coated Balloon

Insight into the study of some nonlinear evolution problems: Applications based on Variation Iteration Method with Laplace

Mathematical modeling and simulation of biophysics systems using neural network

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