add electric field example

examples/examples/expression.rs

@@ -1 +1,43 @@
-fn main() {}
+// we compute the work W associated to the force exerted on a charged particle by an electric field
+//
+// electric field E(x) = E0 / x
+// force exerted  F(x) = q * E0 / x
+//
+// we compute the work done by this force over the displacement from x=a to x=b with:
+//
+// - E0 = 100    V/m
+// - a  = 0.1    m
+// - b  = 0.5    m
+// - q  = 1.0e-6 C
+
+use integraal::{ComputeMethod, DomainDescriptor, FunctionDescriptor, Integraal};
+
+const E0: f64 = 100.0;
+const Q: f64 = 1.0e-6;
+const EXPECTED: f64 = 1.6094379124341003e-4;
+
+fn main() {
+    let domain = DomainDescriptor::Uniform {
+        start: 0.1,
+        step: 1.0e-5,
+        n_step: 40_001,
+    };
+    let function = FunctionDescriptor::Closure(Box::new(|x| Q * E0 / x));
+    let method = ComputeMethod::Trapezoid;
+
+    let mut integraal = Integraal::default()
+        .domain(domain)
+        .function(function)
+        .method(method);
+
+    let Ok(res) = integraal.compute() else {
+        unreachable!()
+    };
+
+    let abs_diff = (res - EXPECTED).abs();
+    assert!(abs_diff < 10e-5);
+
+    println!("expected: {:.18}", EXPECTED);
+    println!("computed: {:.18}", res);
+    println!("diff:    >{:.18}", abs_diff);
+}