This article considers a nonlinear INVERSE problem of the Ostrovsky–Burgers equation by using noisy data. Two B-Splines with different levels, the quintic B-spline and septic B-spline, are used to study this problem. For both B-splines, the stability and convergence analysis are calculated, and results show that an excellent estimation of the unknown functions of the nonlinear INVERSE problem.

In this study, the concept of an INVERSE MATRIX including fuzzy number elements is extended. Such a concept may be performed in the modeling of uncertain and imprecise real-world problems. The problem of finding a fuzzy INVERSE MATRIX is converted to a problem to solve a system of fuzzy polynomial equations. Here, a fuzzy system is transformed to an equivalent system of crisp polynomial equations. The solution of the system of crisp polynomial equations is calculated using Wu’ s method and is introduced a criterion for invertibility of a fuzzy MATRIX (FM). In addition, an algorithm is proposed to calculate the fuzzy INVERSE MATRIX. The most important advantage of the presented method is that it achieves whole INVERSE entries of an FM, simultaneously. In the end, we give some illustrative examples to show the efficiency and proficiency of our proposed algorithm.

In this article, we study the linear INVERSE problem for approximating a timewise-dependentfunction in the second-order hyperbolic equation. To solve the problem, information such as Neumannboundary conditions along with an integral condition and initial conditions at the initial moment and thefinal instant have been provided. In the first step, we show that this problem has a unique solution. Then,we change the main problem into a new one and then we present the spectral APPROXIMATION based onthe Ritz-collocation method to recover the unknown functions. Discretization of the problem by usingthe presented technique leads to a linear system of algebraic equations, which Tikhonov’s regularizationmethod is used to obtain stable solutions. The results of the numerical simulation confirm the high accuracyand stability of the approximate solution.

In this work, we focus on the final value problem of an INVERSE problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi)$. We obtain an approximated solution using the Fourier method and the final input data $L^{r}(0,\pi)$ for $r \neq 2$. Using embedding between $L^{r}(0,\pi)$ and Hilbert scales $\mathcal{H}^{\rho}(0,\pi)$, this study is the error between the exact and regularized solutions to be estimated in $L^{r}(0,\pi)$.