A non-classical sinc-collocation method for the solution of singular boundary value problems arising in physiology

In this paper, a nonclassical sinc collocation method is constructed to the numerical solution of systems of second-order integro-differential equations of Volterra and Fredholm types. The novelty of the approach is based on using the new non classical weight function for sinc method instead of the classic ones. The sinc collocation method based on non classical weight functions is used to reduce the system of integro-differential equations to a system of algebraic equations which can be solved numerically. Furthermore, the convergence of the method is proposed theoretically which shows that the method converges exponentially. By solving some examples numerically, the results are compared with other methods to demonstrate the efficiency of the new method.

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“…To be used in the next sextion, we will recall the following results, taken from [21,23,[28][29][30][31].…”

Section: Sinc Function Preliminariesmentioning

confidence: 99%

“…Using the nonclassical sinc basis functions, f (x) can be approximated on the whole real line as follows [30]…”

Section: )mentioning

confidence: 99%

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Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method

Ghasemi

Mohammadi

Alipanah

2023

Preprint

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“…Convergence rate estimation for functions having a singularity at an endpoint with poly-Sinc discontinuous Galerkin methods is discussed in [12]. A non-classical sinc-collocation method for the solution of singular boundary value problems arising in physiology is discussed in [13]. Numerical solution of third-order boundary value problems using non-classical sinc-collocation method is expressed in [14].…”

Section: Introductionmentioning

confidence: 99%

Sinc approximation for solving fourth-order pseudo-Poisson equations

Majed Al-haliji

2024

J. Al-Qadisiyah Comp. Sci. Math.

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In this article, we will investigate the Galerkin sinc approximation to solve the single pseudo-Poisson problem and in this method we will reach a linear system. We will solve this system by carefully choosing the length of the steps and the number of nodal points and with two methods; the first method, which is the usual method, is theoretically flawed and not practical and computationally efficient. Therefore, to solve the mentioned system, we introduce the orthogonalization technique, which solves both theoretical and computational problems. Numerical approximation is obtained whose accuracy is exponential and of order where N is a transaction parameter and c is a constant independent of N. In the final part, we give some numerical examples of individual pseudo-Poisson problems to demonstrate the efficiency of the method.

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Numerical solution of the system of second-order integro-differential equations using non-classical double sinc method

Mohammadi

Alipanah

2023

Results in Applied Mathematics

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A non-classical sinc-collocation method for the solution of singular boundary value problems arising in physiology

Cited by 8 publications

References 42 publications

Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method

Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method

Sinc approximation for solving fourth-order pseudo-Poisson equations

Numerical solution of the system of second-order integro-differential equations using non-classical double sinc method

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