# Ordinary differential equations

Xem 1-20 trên 72 kết quả Ordinary differential equations
• ### Bài giảng chương 5: Phương trình vi phân - ThS. Hồ Thị Bạch Phương

Mục tiêu của bài giảng "Phương trình vi phân" của ThS. Hồ Thị Bạch Phương nhằm giúp các em sinh viện biết cách giải phương trình vi phân (Ordinary Differential Equations ODEs); Hiểu được tầm qua trọng của phương pháp số giải ODEs; Đánh giá độ tin cậy của các phương pháp đó. Mời quý thầy cô và các em cùng tham khảo chi tiết bài giảng tại đây.

• ### Ebook Numerical recipes in Fortran 77: The art of scientific computing (Volume 1 of Fortran Numerical recipes) – Part 2

(BQ) Ebook Numerical recipes in Fortran 77: The art of scientific computing (Volume 1 of Fortran Numerical recipes) – Part 2 presents the following content: Fast fourier transform, fourier and spectral applications, statistical description of data, modeling of data, integration of ordinary differential equations, two point boundary value problems, integral equations and inverse theory, partial differential equations, less-numerical algorithms.

• ### Synchronization in complete networks of ordinary differential equations of fitzhugh-nagumo type with nonlinear coupling

Synchronization is a ubiquitous feature in many natural systems and nonlinear science. This paper studies the synchronization in a complete network consisting of n nodes. Each node is connected to all other nodes by nonlinear coupling and represented by an ordinary differential system of FitzHugh-Nagumo type (FHN) which can be obtained by simplifying the famous Hodgkin-Huxley model.

• ### Simulation of several flying situations of paragliders

This article represents the mathematical modeling and simulation of several common flying situations of a paraglider through establishing and solving the governing differential equations in state-space. Those flying situations include the ones with constant headwind/tailwind with or without constant upwind; the ones with different scenario for the variations of headwind and tailwind combined with the upwind; the ones with varying pilot mass; and the ones whose several parameters are in the form of interval quantities.

• ### Vibration under variable magnitude moving distributed masses of non-uniform bernoulli–euler beam resting on pasternak elastic foundation

The dynamic response to variable magnitude moving distributed masses of simply supported non-uniform Bernoulli–Euler beam resting on Pasternak elastic foundation is investigated in this paper. The problem is governed by fourth order partial differential equation with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem.

• ### Identical synchronization in complete network of ordinary differential equations of fitzhugh-nagumo

Synchronization is a ubiquitous feature in many natural systems and nonlinear science. In this paper, the synchronization in complete network consisting of n nodes is studied. Each node is connected to all other nodes by linear coupling and it is represented by a system of ordinary differential equations of FitzHugh-Nagumo type which is obtained by simplifying the famous Hodgkin-Huxley model.

• ### Admissible inertial manifolds for abstract nonautonomous thermoelastic plate systems

One of effective approaches to the study of long - time behavior of infinite dimensional dynamical systems is based on the concept of inertial manifolds which was introduced by C. Foias, G. Sell and R. Temam (see [4] and the references therein). These inertial manifolds are finite dimensional Lipschitz ones, attract trajectories at exponential rate. This enables us to reduce the study of infinite dimensional systems to a class of induced finite dimensional ordinary differential equations.

• ### A unified port-hamiltonian approach for modelling and stabilizing control of engineering systems

This paper deals with the port-based modelling of general engineering systems [1] whose dynamics are described by a set of Ordinary Differential Equations (ODEs) and affine in the control input u.

• ### Summary of Phd thesis: Solving some nonlinear boundary value problems for fourth order differential equations

The thesis proposes a simple but very effective method to study the unique solvability and an iterative method for solving five boundary value problems for nonlinear fourth order ordinary differential equations with different types of boundary conditions and two boundary value problems for a biharmonic equation and a biharmonic equation of Kirchhoff type by using the reduction of these problems to the operator equations for the function to be sought or an intermediate function.

• ### Estimate hidden dynamic profiles of siRNA effect on apoptosis

For the representation of RNA interference (RNAi) dynamics, several mathematical models based on systems of ordinary differential equations (ODEs) have been proposed. These models consist of equations for each molecule that are involved in RNAi phenomena.

• ### Rational selection of experimental readout and intervention sites for reducing uncertainties in computational model predictions

Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data.

• ### CRA toolbox: Software package for conditional robustness analysis of cancer systems biology models in MATLAB

In cancer research, robustness of a complex biochemical network is one of the most relevant properties to investigate for the development of novel targeted therapies. In cancer systems biology, biological networks are typically modeled through Ordinary Differential Equation (ODE) models.

• ### Differences in predictions of ODE models of tumor growth: A cautionary example

While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.

• ### Differential calculus notes on wrapped exponential distribution

This work considers the generation of ordinary differential equations whose solutions are the probability functions of wrapped exponential distribution. This will help in understanding the nature of exponential distribution when wrapped in a circle.

• ### An in silico exploration of combining Interleukin-12 with Oxaliplatin to treat liver-metastatic colorectal cancer

Combining anti-cancer therapies with orthogonal modes of action, such as direct cytotoxicity and immunostimulatory, hold promise for expanding clinical benefit to patients with metastatic disease.

• ### Different ODE models of tumor growth can deliver similar results

Simeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology. The model is based on a system of ordinary differential equations (ODEs), and accommodates a lag in therapeutic action through delay compartments.

• ### Effect of radiation and chemical reaction on heat and mass transfer of MHD visco - elastic fluid flow over an exponentially stretching sheet through porous medium

In this paper, we analyze the heat and mass transfer of MHD visco-elastic flow through porous medium in presence of thermal radiation and chemical reaction over an exponentially stretching sheet. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations. By using Homotopy Analysis Method (HAM), the transformed equations are solved analytically.

• ### Radiation and chemical reaction effects on the boundary layer MHD casson fluid on a vertical plate embedded in the porous medium

The present paper is concerned to analyse the magnetohydrodynamic (MHD) Casson fluid flow free convection boundary layer flow of an incompressible electrically conducting fluid through a porous medium subjected to magnetic field in the presence of radiation and chemical reaction. Similarity variables are used to transform the non-linear governing equations are reduced to ordinary partial differential equations, solved by shooting process with BVP4C

• ### Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives

In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Gru¨nwald–Letnikov definition.

• ### Application of the KANTBP 4M program for analysis of models of the low dimensional quantum systems

In the paper, a calculating program named “KANTBP 4M – A program for solving boundary problems of the self-adjoint system of ordinary second order differential equations” is presented.