Numerical solutions of chemical differential-algebraic equations

  title={Numerical solutions of chemical differential-algebraic equations},
  author={Ercan Çelik and Erdal Karaduman and Mustafa Bayram},
  journal={Appl. Math. Comput.},
Numerical solution of differential-algebraic equation systems and applications
The numerical solution of partial differential-algebraic equations
In this paper, a numerical solution of partial differential-algebraic equations (PDAEs) is considered by multivariate Padé approximations. We applied this method to an example. First, PDAE has been
An algorithm for solving DAEs with mechanization
Extension of the differential transformation method to nonlinear differential and integro-differential equations with proportional delays
In this paper, the differential transformation method is applied by providing new theorems to develop exact and approximate solutions of nonlinear differential and integro-differential equations with
A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method
We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula. The solution methodology
Adaptive LMS power series analytical solution for differential algebraic equations
The efficient and accurate solutions provided by the technique proposed are illustrated through simulated examples and it is shown that the performance of the technique proposes outperforms existing conventional and modern methods.
On the Numerical Solution of Generalized Pantograph Equation
Absrtact: In this study, a numerical algorithm for solving a generalization of a functional differential equation known as the pantograph equation is presented. Firstly, the proposed algorithm
Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
In this work, we study the fractional order Lane-Emden differential equations by using the reproducing kernel method. The exact solution is shown in the form of a series in the reproducing kernel
On the numerical solution of differential equations of Lane-Emden type


Approximation methods for the consistent initialization of differential-algebraic equations
The consistency requirement is characterized by a system of equations, an approximation method is introduced for these equations, and the numerical solution of the resulting system is analyzed for certain important classes of DAEs.
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The
One-step and extrapolation methods for differential-algebraic systems
SummaryThe paper analyzes one-step methods for differential-algebraic equations (DAE) in terms of convergence order. In view of extrapolation methods, certain perturbed asymptotic expansions are
Computer methods for ordinary differential equations and differential-algebraic equations
This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications.
Solving Ordinary Differential Equations Using Taylor Series
The included Taylor series method executes faster and yields a more accurate answer than the standard methods for most of the problems in the test set and is most attractwe for small systems and for stringent accuracy tolerances.
Numerical solution of initial-value problems in differential-algebraic equations
The DAE home page introduces theoretical advances Numerical analysis advancements DAE software DASSL Supplementary bibliography Index.