A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resu...

A good understanding of the mathematical processes solving first-order linear ordinary differential equations (ODEs) is foundation for undergraduate students in science and engineering programs to progress smoothly advanced ODEs and/or partial (PDEs) later. However, different methods are presented various textbooks resources, which often confuses their choice method...

Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers’ (PSTs) errors and misconceptions apropos ODEs. analyzed the nature made a te...

in this paper we study the boundary layer problems in which boundary conditions are non-local. here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. by getting help from these conditions, at first the boundary condition is changed from non-local to local. the main aim of this paper is to identify the location of the boundary layer. in ot...

in the present study, vibration of cylindrical laminates with different layers and angles were studied. in order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. laminates were assumed long enough so that plane strain state analysis in 2d can be used properly. in order to satisfy the boundary conditions, variables in terms of fo...