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Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

Malaschonok, Natasha (2007)

Serdica Journal of Computing

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006We produce a parallel algorithm realizing the Laplace transform method for the symbolic solving of differential equations. In this paper we consider systems of ordinary linear differential equations with constant coefficients, nonzero initial conditions and right-hand parts reduced to sums of exponents with polynomial coefficients.

Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method

Yu Ping Wang, Shahrbanoo Akbarpoor Kiasary, Emrah Yılmaz (2024)

Applications of Mathematics

We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.

Some algebraic fixed point theorems for multi-valued mappings with applications

Bupurao C. Dhage (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.

Some classes of linear n th-order differential equations

Valter Šeda (1997)

Archivum Mathematicum

Sufficient conditions for the n -th order linear differential equation are derived which guarantee that its Cauchy function K , together with its derivatives ∂ i K ∂ t i , i = 1 , ⋯ , n - 1 , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.

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