Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

In this paper, first and second order sliding mode controllers are designed for a single link robotic arm actuated by two Pneumatic Artificial Muscles (PAMs). A new mathematical model for the arm has been developed based on the model of large scale pneumatic muscle actuator model. Uncertainty in parameters has been presented and tested for the two controllers. The simulation results of the second-order sliding mode controller proves to have a low tracking error and chattering effect as compared to the first order one. The verification has been done by using MATLAB and Simulink software.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.