It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundstrom theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resul...

In this work, some novel approximate analytical and numerical solutions to the forced damped driven nonlinear (FDDN) pendulum equation relation equations of motion on pivot vertically for arbitrary angles are obtained. The approximation is derived in terms Jacobi elliptic functions with modulus. For approximations, Chebyshev collocation method introduced analyzing motion. Moreover, using MATHEM...

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- boundary-value problems with singularity at time t=0. main objective this paper is make use some mathematical analytic tools techniques order numerically solve reaction–diffusion equations, spherical catalysts biocatalysts, by applying Chebys...

The paper details the use of a nonperturbation successive linearization method to solve the coupled nonlinear boundary value problem due to double-diffusive convection from an inverted cone. Diffusion-thermo and thermal-diffusion effects have been taken into account. The governing partial differential equations are transformed into ordinary differential equations using a suitable similarity tra...

Abstract This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up new Hilbert space that satisfies initial and boundary conditions. collocation applied obtain precise numerical approximation using basis functions based on shifted first-kind ...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems FDEs. The main goal method is convert FDE into a system algebraic equations that can be easily solved using matrix methods. In order achieve this, we first generate operational matrices for fractional integration and block-pulse functions (BPF) function approximation. Since obtained sparse, numerical fast...