On a Mixed Problem for a Parabolic Type Equation with General form Constant Coefficients Under Inhomogeneous Boundary Conditions
Issue:
Volume 11, Issue 3, June 2023
Pages:
32-39
Received:
11 December 2022
Accepted:
11 January 2023
Published:
9 June 2023
Abstract: In this work, we study a one-dimensional mixed problem for an inhomogeneous parabolic equation with constant coefficients of general form, under non-local and non-self-conjugate boundary conditions. The considered mixed problem consist of two parts. The first problem is a mixed problem with a regular boundary condition, and the uniqueness of the solution is proved through the deduction operator. Then the existence of a solution to the mixed problem is shown, and an exact formula for the solution is found. A second mixed problem is the time delay in the boundary conditions. Since the spectral problem obtained after the integral transformation is not homogeneous, the considered problem is again divided into two problems. Under the minimum conditions at the initial data, by combining the deduction method and the contour integral method, the existence and uniqueness of the solution to the mixed problem is proved, where an explicit analytic representation for it is obtained.
Abstract: In this work, we study a one-dimensional mixed problem for an inhomogeneous parabolic equation with constant coefficients of general form, under non-local and non-self-conjugate boundary conditions. The considered mixed problem consist of two parts. The first problem is a mixed problem with a regular boundary condition, and the uniqueness of the so...
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Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect
Omamoke Ekakitie,
Funakpo Isaac,
Olugbenro Osinowo,
Sylvester Chibueze Izah,
Keneke Edwin Dauseye,
Bunonyo Wilcox Kubugha
Issue:
Volume 11, Issue 3, June 2023
Pages:
40-51
Received:
14 March 2023
Accepted:
6 April 2023
Published:
20 June 2023
Abstract: Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.
Abstract: Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a r...
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Numerical Simulation of the Heat Equation Using RBF Collocation Method
Antoine Filankembo Ouassissou,
Den Matouadi,
Cordy Jourvel Itoua-Tsele
Issue:
Volume 11, Issue 3, June 2023
Pages:
52-57
Received:
5 May 2023
Accepted:
5 June 2023
Published:
20 June 2023
Abstract: For a very long time, finite volume, finite element, or finite difference methods have been used to solve partial differential equations (PDEs) numerically. These techniques have been used by researchers for centuries to solve a wide range of mathematical, physical, or chemical problems. The complexity of these numerical approaches, for the resolution of the PDEs in space dimensions equal to two or higher, can come from the coding, the management, and the good choice of the triangulation or the mesh of the domain in which one wishes to locate the solution. The radial basis function collocation method is a meshless technique used to numerically solve some partial differential equations and is based on the nodes of the domain and a radial basis function is a real-valued function whose value only depends on the separation of its input parameter x from another fixed point, sometimes known as the function's origin or center. This method was introduced by KANSA in the 1990s. In this study, the numerical simulation of the one-dimensional heat equation was carried out using the RBF Collocation Method and particularly the Gaussian function. This model was used to test the accuracy and efficiency of this method by comparing numerical and analytical solutions on rectangular geometry with collocation nodes. The results show that the RBF collocation approximate solution and the exact solution coincided in test case problems 2, 3 and 4.
Abstract: For a very long time, finite volume, finite element, or finite difference methods have been used to solve partial differential equations (PDEs) numerically. These techniques have been used by researchers for centuries to solve a wide range of mathematical, physical, or chemical problems. The complexity of these numerical approaches, for the resolut...
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