In this paper, coupled nonlinear Burgers’ equations are solved through a variety of meshless methods known as multiquadric quasi-interpolation scheme. In this scheme, the extension of univariate quasi-interpolation method is used to approximate the unknown functions and their spatial derivatives and the Taylor series expansion is used to discretize the temporal derivatives. The multiquadric qua...

This note concerns density properties of the general multiquadric, (x + c2)k−1/2, where k is a fixed natural number. We establish that scattered translates of the general multiquadric are dense in C([a, b]), where a and b are finite. As a corollary, we show that scattered translated of the general multiquadric are dense in the function spaces L([a, b]), for 1 ≤ p <∞.

Abstract. Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data. Notwithstanding, RBFs pose computational challenges, such as the efficient evaluation of an n-center RBF expansion at m points. A direct summation requires O(nm) operations. We present a new multilevel method whose cost is only O((n + m) ln(1/δ)), where δ is the desired a...

This paper applies the global radial basis functions as a spatial collocation scheme for solving the Options Pricing model. Diierent numerical time integration schemes are employed for the time derivative of the model. It is shown that the major numerical error is from the time integration instead of the spatial approximation by comparing with the analytical solution. Since the basis functions ...

Lesion mimic mutants display spontaneous necrotic spots and chlorotic leaves as a result of mis-regulated cell death programmes. Typically these mutants have increased resistance to biotrophic pathogens but their response to facultative fungi that cause necrotrophic diseases is less well studied. The effect of altered cell death regulation on the development of disease caused by Ramularia collo...

A computational algorithm based on the multiquadric, which is a continuously diierentiable radial basis function, is devised to solve the shallow-water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any diierence scheme. The method does not requ...

In this paper, an interpolation method for solving linear diierential equations was developed using multiquadric scheme. Unlike most iterative formula , this method provides a global interpolation formulae for the solution. Numerical examples show that this method ooers a higher degree of accuracy than Runge-Kutta formula and the iterative multistep methods developed by Hyman (1978).

In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1){ y′(t) = f(t, y(t), y(t− τ(t, y(t))), y′(t− σ(t, y(t)))), t1 ≤ t ≤ tf , y(t) = φ(t), t ≤ t1, where f : [t1, tf ] × R × R × R → R is a smooth function, τ(t, y(t)) and σ(t, y(t)) are continuous functions on [t1, tf ]×R such that t−τ(t, y(t)) < tf and t− σ(...