In this paper, we analyze a new form of non-local boundary conditions for a two-dimensional elliptic partial differential equation model. Some relations for the existence of the different types of eigenvalues and their corresponding eigenfunctions are proved. The figures of the relations are also dragged to show the effect of the non-locality in boundary conditions on the eigenvalue problem.

The aim of this article is to present an efficient numerical procedure for solving higher-order linear delay differential equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. Four problems are solved and results are compared with the existing results to show the accuracy and applicability of Laguerre polynomials.

A new approach implementing the cubic B-spline technique is introduced for the numerical solution of a class of singular partial differential equation. Properties of these cubic B-spline functions are first presented. These properties are then used to reduce singular partial differential equation to systems of linear algebraic equations. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems. The examples include regular and singular problems.

The different methods used in the multiplication of numbers are long method (column method) of multiplication, grid methods and addition methods of multiplication. The utilization of the methods mentioned to solve power (index) of base number (number that multiply itself in a number of times) are horrendous, outrageous, tedious, time consuming and too long to be carried out. This study develops computation of the power of base of number using Kifilideen (matrix, combination and distributive (MCD)) approach. The Kif matrix method of multiplication is a shorter version of the long method (column method) of multiplication. The matrix method provides a straight forward, direct and systematic means of multiplication of digit number that multiply itself repetitively.

The extracellular signal-regulated protein kinase (ERK), a subfamily of Mitogen-Activated Protein Kinase (MAPK) pathways, is one of the most important signals in the regulation of many biological processes. Deregulated of MAPK signaling pathways has been observed in human cancers with potential involvement in most of all cellular processes leading to tumorigenesis so that it became a potential target for therapy in cancer patients. In this paper, we discuss a Mathematical model of ERK activation in the presence of a small molecule inhibitor that competes with RAS. We present analytical expressions for the concentration of RAS, complex RAS-ERK, complex RAS-Inhibitor, and activated ERK in terms of dimensionless parameters using He’s Homotopy Perturbation Method (HPM). The analytical results are compared with numerical simulation and satisfactory agreement is obtained.

We discuss tri-quasi ideals and bi-quasi ideals in ternary semigroups and give some characterizations. The intersection of left, lateral and right ideals is a tri-ideal and product of left, lateral and right ideals is again a tri-ideal. We also discuss m-tri-ideals towards some characterizations in terms of tri-ideals. Some relevant counter examples are also indicated.

In this paper, we consider a mathematical model of Rabies disease which is an infectious disease. The model we are considering is a system of nonlinear ordinary differential equations and it is difficult to find an exact solution. He’s Homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear ordinary differential equations. The findings obtained by HPM are compared with a nonstandard finite difference (NSFD) and Runge-Kutta fourth order (RK4) methods. Some plots are presented to show the reliability and simplicity of the method.

In this paper, an improved technique is presented to recover the fi- nite element gradient at boundaries. The proposed technique begins by evaluating the recovered gradient at the interior nodes using polynomial preserving recovery technique. Then we propose formula for weights to the recovered gradient at the interior nodes attached to boundary nodes. The sum of these weighted recovered gradients is utilized as an approxi- mation for the gradient at the attached boundary node. The validity of the proposed technique is illustrated by some two-dimensional numerical examples.

This paper is attempted to study the system of nonlinear differential equations in assessing the depletion of forest resource with population density and industrialization. It is evidenced that the forest resources are depleted with increase of population and industrialization. The asymptotic method of differential equations and numerical simulation are used to analyze this model. These analytical results are confirmed by using numerical simulation. Further, the graph of proposed model is compared with the real life data of the forestry resources, population density and industrialization in Tamil Nadu.

In this paper we utilize the finite element method for solving random nonlinear differential equations. In the proposed technique, the nodal coefficients are formulated as functions of the random variable. At certain values of random variable, curve fitting is used to construct the approximate nodal solution. Several numerical examples are presented, and the approximate mean solutions are compared with the exact mean solution to illustrate the ability and effectiveness of this method.