Block-Pulse functions are zero-order B-splines, which can be use only for function interpolation/approximation. But some people apply them for differential equations!!!!
which is a very big mistake.
What do you mean by combining a 0-order B-spline with the other B-splines?
I believe(wrong or true! i don't know and this is my question) that i can mix b splines with block pulse or haar functions to gain a hybrid function to approximate time delay control systems but i should change b splines to orthonormal basis function and then do so.
"hybrid" has some meanings in numerical methods. One can decompose the underlying domain in to two parts and use different trial spaces in each sections. for example in "hybrid BEM-FEM" a part of domain is treated with boundary element method (BEM) and the remain part by finite element method (FEM). there may be some other hybrid strategies.
What do you exactly mean by "hybrid" in your question?
By the way, when you combine two techniques, you should gain some benefits which can not be achieved when the techniques are applied separately.
thanks again for your answer. you are right. hybrid should gain some benefits and my idea exactly is this but if you are familiar with hybrid of block pulse with Legendre or block pulse with Taylor or block pulse with chebycheve functions, i would like to do so. if you aren't familiar i can send some papers for you. now my question is:' can i do like that papers with block pulse and Bsplines?"