A FIRST ORDER ACCURACY SCHEME ON NON-UNIFORM MESH

Mirjana Stojanovi\'c

Abstract: It is proved that the exponentially fitted quadratic spline difference scheme derived in [5] and applied to the singularly perturbed two-point boundary value problem $$ \aligned &\varepsilon y''+p(x)y'=f(x),\quad 0 & y(0)=\alpha_1,\; y(1)=\alpha_1,\; p(x)\ge p>0. \endaligned $$ has the first order of uniform convergence on non-uniform mesh. In order to achieve the uniform first order accuracy the special almost uniform mesh which satisfies the condition $h_i=h_{i-1}+Mh_{i-1}\max(x_i,\varepsilon)$ was constructed. The results are illustrated by numerical experiments.

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