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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.

Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions

Chein-Shan Liu, Botong Li (2019)

Applications of Mathematics

For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly...

Currently displaying 281 – 300 of 897