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In the current work, a new reproducing kernel method (RKM) for solving nonlinear forced Duffing equations with integral boundary conditions is developed. The proposed collocation technique is based on the idea of RKM and the orthonormal Bernstein polynomials (OBPs) approximation together with the quasi-linearization method. In our method, contrary to the classical RKM, there is no need to use the Gram-Schmidt orthogonalization procedure and only a few nodes are used to obtain efficient numerical results. Three numerical examples are included to show the applicability and efficiency of the suggested method. Also, the obtained numerical results are compared with some results in the literature. [ABSTRACT FROM AUTHOR]

An important equation usually used in modeling neuronal dynamics is cable equation. In this work, a numerical method for the fractional cable equation which involves two Riemann-Liouville fractional derivatives is proposed. Our computational technique is based on collocation idea where a combination of Bernoulli polynomials and Sinc functions are used to approximate the solution to this problem. The constructed approximation by our method convert the fractional cable equation into a set of algebraic equations. Also, we provide two numerical examples to confirm the accuracy and effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This work presents a new approximation approach to solve the linear/nonlinear distributed order fractional differential equations using the Chebyshev polynomials. Here, we use the Chebyshev polynomials combined with the idea of the collocation method for converting the distributed order fractional differential equation into a system of linear/nonlinear algebraic equations. Also, fractional differential equations with initial conditions can be solved by the present method. We also give the error bound of the modified equation for the present method. Moreover, four numerical tests are included to show the effectiveness and applicability of the suggested method. [ABSTRACT FROM AUTHOR]

An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated. The steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition. The resulting nonlinear boundary value problem is solved using quintic B-spline collocation and sinc-collocation methods. The approach consists of reducing the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the techniques and a comparison is made with existing results in the literature. [ABSTRACT FROM PUBLISHER]