مجله بین المللی محاسبات و مدل سازی ریاضی
سال سیزدهم شماره 2 (Spring 2023)

In this paper;, ;we investigate the symmetry group of the (3 + 1)-;dimensional Sakovich equation;. ;We obtain the classical and non-classical Lie symmetries for the equation under consideration;. Therefore;, ;we respond to the question of classification of the equation symmetries and;, ;as a result;, ;its invariant solutions;. Presenting the algebra of symmetries and utilizing Ibragimov’s method;, ;we create the optimal system of Lie subalgebras;. ;We obtain the symmetry reductions and invariant solutions of the considered equation using these vector fields;.

In this paper, we present a class of exact solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere. The field equations are integrated by specifying the forms of the electric field, anisotropic factor, and one of the gravitational potentials which are physically reasonable. By reducing the condition of pressure isotropy to a linear, second order differential equation which can be solved in general, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. The solution is regular, well behaved and complies with all the requirements of a realistic stellar model. An interesting feature of the new class of solutions is that one can easily switch off the electric and/or anisotropic effects in this formulation. Consequently, we regain some of the earlier solutions.

In this paper, we prove some fixed point theorems for finite family of G-monotone generalized quasi contraction mappings in a metric space endowed with a graph. Example is provided to show the effectiveness of our results.

In this paper, a nonlinear mathematical model of COVID-19 was developed. An SVEIHR model has been proposed using a system of ordinary differential equations. The model’s equilibrium points were found, and the model’s stability analysis and sensitivity analysis around these equilibrium points were investigated. The model’s basic reproduction number is investigated in the next-generation matrix. The disease free equilibrium of the COVID-19 model is stable if the basic reproduction number is less than unity; if the basic reproduction number is greater than unity, the disease free equilibrium is unstable. We also utilize numerical simulation to explain how each parameter affects the basic reproduction number.

In this paper we use numerical methods to investigate the Casimir effect for a scalar field in a specific boundary condition. In order to calculate the energy-momentum tensor, the holographic method is used, and, the background is Schrodinger-type metric which is close to the classical metric. We also compute the holographic entanglement entropy, and, for two steps the mutual information is also studied. By numerical analysis, we argue that the mutual information is always positive. Furthermore, for three entangling regions, we show that the corresponding tripartite information becomes negative.

In this research;, ;using the multiplier method and the 2-dimensional; homotopy operator;, ;higher order conservation laws for the; ;Hunter-Saxton equation are computed;. ;Also;, ;in order to construct new; ;conservation laws;, ;the invariance properties of the multipliers are; ;studied using Lie classical symmetries;.