This paper is concerned with the inverse spectral problem for third-order differential equation distribution coefficient. The consists in recovery of expression coefficients from data two boundary value problems separated conditions. For this problem, we solve most fundamental question theory about necessary and sufficient conditions solvability. In addition, prove local solvability stability p...

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...

The most up-to-date version of this collection of homework exercises can always be found at 1. Find the general solution for the following first-order partial differential equation. 3u x + 5u y − xyu = 0 2. Find the general solution for the following first-order partial differential equation. u x − u y + yu = 0 3. Find the general solution for the following first-order partial differential equa...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...