Error analysis of the Chebyshev collocation method for linear second-order partial differential equations

Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

“…The upper bound for the second term can be found by adding and subtracting the polynomial ( , +1 ) following the work in [20].…”

“…Chebyshev polynomials were proposed by the Russian mathematician Chebyshev. Many authors depend on Chebyshev collocation method to solve different types of equations such as linear differential equations [13], systems of highorder linear differential equations with variable coefficients [14], systems of high-order linear Fredholm-Volterra integrodifferential equations [15], fourth-order Sturm-Liouville problems [16], Troeschs problem [17], nonlinear differential equations [18], linear partial differential equations [19,20], and nonlinear Fredholm-Volterra integrodifferential equations [21]. This paper is organized into six sections.…”

Numerical Solution of Two Dimensional Laplace’s Equation on a Regular Domain Using Chebyshev Differentiation Matrices

“…Weideman and Reddy [3] published a book on MATALAB differentiation matrix suite based on pseudospectral method. Yuksel et al [7] applied apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. Sahuck [8] used Chebyshev collocation method to solve multi-dimensional partial differential equations where efficient calculations are conducted by converting dense systems of equations to sparse using the quasiinverse technique and separating coupled spectral modes using the matrix diagonalization method.…”

Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions

“…In recent years, some research works have been focused on the application of collocation methods for solving linear one-dimensional parabolic and hyperbolic (specially Telegraph equations) PDEs such as Chebyshev collocation method [12] and Bessel collocation method [13,14]. But application of this scheme for solving multidimensional PDEs has had few results.…”