we present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. numerical method of sixth-order with end conditions of the order 6 is derived. the convergence analysis of the method has been discussed. numerical examples are presented to illustra...

Abstract In this paper we refer to the reconstruction formulas given in Andersson’s On the determination of a function from spherical averages, which are often used in applications such as SAR1 and SONAR2. We demonstrate that the first one of these formulas does not converge given physically reasonable assumptions. An alternative is proposed and it is shown that the second reconstruction formul...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...

Taking the equation racing car frame as research object, 3D modeling software was used to establish model of frame, and free mode analysis conducted through finite element software. The natural frequency within range 30-120Hz, avoiding possibility resonance, indicating that structural design reasonable. In addition, vibration analyzed. This provides a certain idea for further optimization frame.